| Type: | Package |
| Title: | Tractable Parametric Odds-Based Regression Models |
| Version: | 0.1.0 |
| Maintainer: | Abdisalam Hassan Muse <abdisalam.h.muse@gmail.com> |
| Description: | Fits tractable fully parametric odds-based regression models for survival data, including proportional odds (PO), accelerated failure time (AFT), accelerated odds (AO), and General Odds (GO) models in overall survival frameworks. Given at least an R function specifying the survivor, hazard rate and cumulative distribution functions, any user-defined parametric distribution can be fitted. We applied and evaluated a minimum of seventeen (17) various baseline distributions that can handle different failure rate shapes for each of the four different proposed odds-based regression models. For more information see Bennet et al., (1983) <doi:10.1002/sim.4780020223>, and Muse et al., (2022) <doi:10.1016/j.aej.2022.01.033>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | AHSurv, flexsurv, pracma, stats, stats4 |
| Depends: | R (≥ 2.10) |
| RoxygenNote: | 7.2.1 |
| NeedsCompilation: | no |
| Packaged: | 2022-09-07 22:05:23 UTC; Admin |
| Author: | Abdisalam Hassan Muse
 [aut, cre],
Samuel Mwalili [aut, ctb],
Oscar Ngesa [aut, ctb],
Christophe Chesneau [aut, ctb] |
| Repository: | CRAN |
| Date/Publication: | 2022-09-08 09:12:56 UTC |
Accelerated Failure Time (AFT) Model.
Description
Tractable Parametric accelerated failure time (AFT) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEAFT(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic accelerated failure time "NGLLAFT" model, generalized log-logisitic accelerated failure time "GLLAFT" model, modified log-logistic accelerated failure time "MLLAFT" model, exponentiated Weibull accelerated failure time "EWAFT" model, power generalized weibull accelerated failure time "PGWAFT" model, generalized gamma accelerated failure time "GGAFT" model, modified kumaraswamy Weibull proportional odds "MKWAFT" model, log-logistic accelerated failure time "LLAFT" model, tangent-log-logistic accelerated failure time "TLLAFT" model, sine-log-logistic accelerated failure time "SLLAFT" model, cosine log-logistic accelerated failure time "CLLAFT" model, secant-log-logistic accelerated failure time "SCLLAFT" model, arcsine-log-logistic accelerated failure time "ASLLAFT" model, arctangent-log-logistic accelerated failure time "ATLLAFT" model, Weibull accelerated failure time "WAFT" model, gamma accelerated failure time "GAFT", and log-normal accelerated failure time "LNAFT") |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEAFT(init = c(1.0,0.20,0.05),times = time,status = delta,n=nrow(z),
basehaz = "WAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEAFT(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEAFT(init = c(1.0,0.50,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LLAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEAFT(init = c(1.0,0.5,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
Accelerated Odds (AO) Model.
Description
A Tractable Parametric Accelerated Odds (AO) model's maximum likelihood estimates,log-likelihood, and Information Criterion values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEAO(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init |
: Initial parameters to maximize the likelihood function; |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic accelerated odds "NGLLAO" model, generalized log-logisitic accelerated odds "GLLAO" model, modified log-logistic accelerated odds "MLLAO" model,exponentiated Weibull accelerated odds "EWAO" model, power generalized weibull accelerated odds "PGWAO" model, generalized gamma accelerated odds "GGAO" model, modified kumaraswamy Weibull accelerated odds "MKWAO" model, log-logistic accelerated odds "LLAO" model, tangent-log-logistic accelerated odds "TLLAO" model, sine-log-logistic accelerated odds "SLLAO" model, cosine log-logistic accelerated odds "CLLAO" model,secant-log-logistic accelerated odds "SCLLAO" model, arcsine-log-logistic accelerated odds "ASLLAO" model,arctangent-log-logistic accelerated odds "ATLLAO" model, Weibull accelerated odds "WAO" model, gamma accelerated odds "WAO" model, and log-normal accelerated odds "ATLNAO" model.) |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEAO(init = c(1.0,0.40,0.50,0.50),times = time,status = delta,n=nrow(z),
basehaz = "GLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "CLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "LNAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEAO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "ASLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
General Odds (GO) Model.
Description
A Tractable Parametric General Odds (GO) model's Log-likelihood, MLE and information criterion values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEGO(
init,
times,
status,
n,
basehaz,
z,
zt,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic general odds "NGLLGO" model, generalized log-logisitic general odds "GLLGO" model, modified log-logistic general odds "MLLGO" model,exponentiated Weibull general odds "EWGO" model, power generalized weibull general odds "PGWGO" model, generalized gamma general odds "GGGO" model, modified kumaraswamy Weibull general odds "MKWGO" model, log-logistic general odds "LLGO" model, tangent-log-logistic general odds "TLLGO" model, sine-log-logistic general odds "SLLGO" model, cosine log-logistic general odds "CLLGO" model,secant-log-logistic general odds "SCLLGO" model, arcsine-log-logistic general odds "ASLLGO" model, arctangent-log-logistic general odds "ATLLGO" model, Weibull general odds "WGO" model, gamma general odds "WGO" model, and log-normal general odds "ATLNGO" model.) |
z |
: design matrix for odds-level effects (p x n), p >= 1 |
zt |
: design matrix for time-dependent effects (q x n), q >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEGO(init = c(1.0,0.50,0.50,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "PGWGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEGO(init = c(1.0,0.50,0.45,0.5),times = time,status = delta,n=nrow(z),
basehaz = "TLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEGO(init = c(1.0,1.0,0.50,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "GLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
Proportional Odds (PO) model.
Description
Tractable Parametric Proportional Odds (PO) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
Usage
MLEPO(
init,
times,
status,
n,
basehaz,
z,
method = "BFGS",
hessian = TRUE,
conf.int = 0.95,
maxit = 1000,
log = FALSE
)
Arguments
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic proportional odds "NGLLPO" model, generalized log-logisitic proportional odds "GLLPO" model, modified log-logistic proportional odds "MLLPO" model, exponentiated Weibull proportional odds "EWPO" model, power generalized weibull proportional odds "PGWPO" model, generalized gamma proportional odds "GGPO" model, modified kumaraswamy Weibull proportional odds "MKWPO" model, log-logistic proportional odds "PO" model, tangent-log-logistic proportional odds "TLLPO" model, sine-log-logistic proportional odds "SLLPO" model, cosine log-logistic proportional odds "CLLPO" model, secant-log-logistic proportional odds "SCLLPO" model, arcsine-log-logistic proportional odds "ASLLPO" model, and arctangent-log-logistic proportional odds "ATLLPO" model, Weibull proportional odds "WPO" model, gamma proportional odds "GPO" model, and log-normal proportional odds "LNPO" model.) |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
Value
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
#Example #1
data(alloauto)
time<-alloauto$time
delta<-alloauto$delta
z<-alloauto$type
MLEPO(init = c(1.0,0.40,1.0,0.50),times = time,status = delta,n=nrow(z),
basehaz = "GLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #2
data(bmt)
time<-bmt$Time
delta<-bmt$Status
z<-bmt$TRT
MLEPO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z),
basehaz = "SLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
#Example #3
data("gastric")
time<-gastric$time
delta<-gastric$status
z<-gastric$trt
MLEPO(init = c(1.0,0.50,1.0,0.75),times = time,status = delta,n=nrow(z),
basehaz = "PGWPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,
log=FALSE)
#Example #4
data("larynx")
time<-larynx$time
delta<-larynx$delta
larynx$age<-as.numeric(scale(larynx$age))
larynx$diagyr<-as.numeric(scale(larynx$diagyr))
larynx$stage<-as.factor(larynx$stage)
z<-model.matrix(~ stage+age+diagyr, data = larynx)
MLEPO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z),
basehaz = "ATLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
New Generalized Log-logistic (NGLL) survivor function.
Description
New Generalized Log-logistic (NGLL) survivor function.
Usage
SNGLL(t, kappa, alpha, eta, zeta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
Value
the value of the NGLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Hassan Muse, A. A new generalized log-logistic distribution with increasing, decreasing, unimodal and bathtub-shaped hazard rates: properties and applications, in Proceedings of the Symmetry 2021 - The 3rd International Conference on Symmetry, 8–13 August 2021, MDPI: Basel, Switzerland, doi:10.3390/Symmetry2021-10765.
Examples
t=runif(10,min=0,max=1)
SNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
Leukemia data set
Description
The alloauto data frame has 101 rows and 3 columns.
Format
This data frame contains the following columns:
time: Time to death or relapse, months
type :Type of transplant (1=allogeneic, 2=autologous)
delta:Leukemia-free survival indicator (0=alive without relapse, 1=dead or relapse)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, abdisalam.hassan@amoud.edu.so
Source
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data, Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
Examples
{
data(alloauto)
str(alloauto)
}
Bone Marrow Transplant (bmt) data set
Description
Bone marrow transplant study which is widely used in the hazard-based regression models
Format
There were 46 patients in the allogeneic treatment and 44 patients in the autologous treatment group
Time: time to event
Status: censor indicator, 0 for censored and 1 for uncensored
TRT: 1 for autologous treatment group; 0 for allogeneic treatment group
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, abdisalam.hassan@amoud.edu.so
References
Robertson, V. M., Dickson, L. G., Romond, E. H., & Ash, R. C. (1987). Positive antiglobulin tests due to intravenous immunoglobulin in patients who received bone marrow transplant. Transfusion, 27(1), 28-31.
Gastric data set
Description
The gastric data frame has 90 rows and variables.It is a data set from a clinical trial conducted by the Gastrointestinal Tumor Study Group (GTSG) in 1982. The data set refers to the survival times of patients with locally nonresectable gastric cancer. Patients were either treated with chemotherapy combined with radiation or chemotherapy alone.
Format
This data frame contains the following columns:
time: survival times in days
trt :treatments (1=chemotherapy + radiation; 0=chemotherapy alone)
status:failure indicator (1=failure, 0=otherwise)
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, abdisalam.hassan@amoud.edu.so
Source
Gastrointestinal Tumor Study Group. (1982) A Comparison of Combination Chemotherapy and Combined Modality Therapy for Locally Advanced Gastric Carcinoma. Cancer 49:1771-7.
Examples
{
data(gastric)
str(gastric);head(gastric)
}
Larynx Cancer-Patients data set
Description
Larynx Cancer-Patients data set which is widely used in the survival regression models
Format
The data frame contains 90 rows and 5 columns:
time: time to event, in months
delta: Censor indicator, 0 alive and 1 for dead
stage: Stage of disease (1=stage 1, 2=stage2, 3=stage 3, 4=stage 4)
diagyr: Year of diagnosis of larynx cancer
age: Age at diagnosis of larynx cancer
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, abdisalam.hassan@amoud.edu.so
References
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data, Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
Arcsine-Log-logistic (ASLL) Cumulative Distribution Function.
Description
Arcsine-Log-logistic (ASLL) Cumulative Distribution Function.
Usage
pASLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the ASLL Cumulative Distribution Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
Examples
t=runif(10,min=0,max=1)
pASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Cumulative Distribution Function.
Description
Arctangent-Log-logistic (ATLL) Cumulative Distribution Function.
Usage
pATLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the ATLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions: Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
Examples
t=runif(10,min=0,max=1)
pATLL(t=t, alpha=0.7, beta=0.5)
Cosine-Log-logistic (SLL) Cumulative Distribution Function.
Description
Cosine-Log-logistic (SLL) Cumulative Distribution Function.
Usage
pCLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the CLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 63-79.
Examples
t=runif(10,min=0,max=1)
pCLL(t=t, alpha=0.7, beta=0.5)
Exponentiated Weibull (EW) Cumulative Distribution Function.
Description
Exponentiated Weibull (EW) Cumulative Distribution Function.
Usage
pEW(t, lambda, kappa, alpha, log.p = FALSE)
Arguments
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
Value
the value of the EW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pEW(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)
Gamma (G) Cumulative Distribution Function.
Description
Gamma (G) Cumulative Distribution Function.
Usage
pG(t, shape, scale)
Arguments
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
Value
the value of the G Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pG(t=t, shape=0.85, scale=0.5)
Generalised Gamma (GG) Cumulative Distribution Function.
Description
Generalised Gamma (GG) Cumulative Distribution Function.
Usage
pGG(t, kappa, alpha, eta, log.p = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
Value
the value of the GG cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
Generalized Log-logistic (GLL) cumulative distribution function.
Description
Generalized Log-logistic (GLL) cumulative distribution function.
Usage
pGLL(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the GLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Muse, A. H., Mwalili, S., Ngesa, O., Almalki, S. J., & Abd-Elmougod, G. A. (2021). Bayesian and classical inference for the generalized log-logistic distribution with applications to survival data. Computational intelligence and neuroscience, 2021.
Examples
t=runif(10,min=0,max=1)
pGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Log-logistic (LL) Cumulative Distribution Function.
Description
Log-logistic (LL) Cumulative Distribution Function.
Usage
pLL(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
Value
the value of the LL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Cumulative Distribution Function.
Description
Lognormal (LN) Cumulative Distribution Function.
Usage
pLN(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
Value
the value of the LN cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pLN(t=t, kappa=0.75, alpha=0.95)
Modified Kumaraswamy Weibull (MKW) Cumulative Distribution Function.
Description
Modified Kumaraswamy Weibull (MKW) Cumulative Distribution Function.
Usage
pMKW(t, alpha, kappa, eta)
Arguments
t |
: positive argument |
alpha |
: Inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
Value
the value of the MKW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
Modified Log-logistic (MLL) cumulative distribution function.
Description
Modified Log-logistic (MLL) cumulative distribution function.
Usage
pMLL(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the MLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model. Applied Bionics and Biomechanics, 2022.
Examples
t=runif(10,min=0,max=1)
pMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
New Generalized Log-logistic (NGLL) cumulative distribution function.
Description
New Generalized Log-logistic (NGLL) cumulative distribution function.
Usage
pNGLL(t, kappa, alpha, eta, zeta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
Value
the value of the NGLL cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Hassan Muse, A. A new generalized log-logistic distribution with increasing, decreasing, unimodal and bathtub-shaped hazard rates: properties and applications, in Proceedings of the Symmetry 2021 - The 3rd International Conference on Symmetry, 8–13 August 2021, MDPI: Basel, Switzerland, doi:10.3390/Symmetry2021-10765.
Examples
t=runif(10,min=0,max=1)
pNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
Power Generalised Weibull (PGW) cumulative distribution function.
Description
Power Generalised Weibull (PGW) cumulative distribution function.
Usage
pPGW(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the PGW cumulative distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival data. Statistics in Medicine, 40(19), 4213-4229.
Examples
t=runif(10,min=0,max=1)
pPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
Secant-log-logistic (SCLL) Cumulative Distribution Function.
Description
Secant-log-logistic (SCLL) Cumulative Distribution Function.
Usage
pSCLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the SCLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A. (2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
Examples
t=runif(10,min=0,max=1)
pSCLL(t=t, alpha=0.7, beta=0.5)
Sine-Log-logistic (SLL) Cumulative Distribution Function.
Description
Sine-Log-logistic (SLL) Cumulative Distribution Function.
Usage
pSLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the SLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the Sin-G class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3), 357-379.
Examples
t=runif(10,min=0,max=1)
pSLL(t=t, alpha=0.7, beta=0.5)
Tangent-Log-logistic (TLL) Cumulative Distribution Function.
Description
Tangent-Log-logistic (TLL) Cumulative Distribution Function.
Usage
pTLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the TLL Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pTLL(t=t, alpha=0.7, beta=0.5)
Weibull (W) Cumulative Distribution Function.
Description
Weibull (W) Cumulative Distribution Function.
Usage
pW(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
Value
the value of the W Cumulative Distribution function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pW(t=t, kappa=0.75, alpha=0.5)
Generalised Gamma (GG) Probability Density Function.
Description
Generalised Gamma (GG) Probability Density Function.
Usage
pdGG(t, kappa, alpha, eta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the GG probability density function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
pdGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Arcsine-Log-logistic (ASLL) Hazard Rate Function.
Description
Arcsine-Log-logistic (ASLL) Hazard Rate Function.
Usage
rASLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the ASLL Hazard Rate Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Arctangent-Log-logistic (ATLL) Hazard Function.
Description
Arctangent-Log-logistic (ATLL) Hazard Function.
Usage
rATLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the ATLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rATLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Cosine-Log-logistic (CLL) Hazard Function.
Description
Cosine-Log-logistic (CLL) Hazard Function.
Usage
rCLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the CLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 63-79.
Examples
t=runif(10,min=0,max=1)
rCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Exponentiated Weibull (EW) Hazard Function.
Description
Exponentiated Weibull (EW) Hazard Function.
Usage
rEW(t, lambda, kappa, alpha, log = FALSE)
Arguments
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the EW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Khan, S. A. (2018). Exponentiated Weibull regression for time-to-event data. Lifetime data analysis, 24(2), 328-354.
Examples
t=runif(10,min=0,max=1)
rEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)
Gamma (G) Hazard Function.
Description
Gamma (G) Hazard Function.
Usage
rG(t, shape, scale, log = FALSE)
Arguments
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the G hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rG(t=t, shape=0.5, scale=0.85,log=FALSE)
Generalised Gamma (GG) Hazard Function.
Description
Generalised Gamma (GG) Hazard Function.
Usage
rGG(t, kappa, alpha, eta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the GG hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Agarwal, S. K., & Kalla, S. L. (1996). A generalized gamma distribution and its application in reliabilty. Communications in Statistics-Theory and Methods, 25(1), 201-210.
Examples
t=runif(10,min=0,max=1)
rGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Generalized Log-logistic (GLL) hazard function.
Description
Generalized Log-logistic (GLL) hazard function.
Usage
rGLL(t, kappa, alpha, eta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the GLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Muse, A. H., Mwalili, S., Ngesa, O., Alshanbari, H. M., Khosa, S. K., & Hussam, E. (2022). Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients. Alexandria Engineering Journal, 61(10), 7953-7978.
Examples
t=runif(10,min=0,max=1)
rGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)
Log-logistic (LL) Hazard Function.
Description
Log-logistic (LL) Hazard Function.
Usage
rLL(t, kappa, alpha, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the LL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)
Lognormal (LN) Hazard Function.
Description
Lognormal (LN) Hazard Function.
Usage
rLN(t, kappa, alpha, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the LN hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)
Modified Kumaraswamy Weibull (MKW) Hazard Function.
Description
Modified Kumaraswamy Weibull (MKW) Hazard Function.
Usage
rMKW(t, alpha, kappa, eta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the MKW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Khosa, S. K. (2019). Parametric Proportional Hazard Models with Applications in Survival analysis (Doctoral dissertation, University of Saskatchewan).
Examples
t=runif(10,min=0,max=1)
rMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)
Modified Log-logistic (MLL) hazard function.
Description
Modified Log-logistic (MLL) hazard function.
Usage
rMLL(t, kappa, alpha, eta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the MLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)
New Generalized Log-logistic (NGLL) hazard function.
Description
New Generalized Log-logistic (NGLL) hazard function.
Usage
rNGLL(t, kappa, alpha, eta, zeta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the NGLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)
Power Generalised Weibull (PGW) hazard function.
Description
Power Generalised Weibull (PGW) hazard function.
Usage
rPGW(t, kappa, alpha, eta, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the PGW hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)
Secant-log-logistic (SCLL) Hazard Function.
Description
Secant-log-logistic (SCLL) Hazard Function.
Usage
rSCLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the SCLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A. (2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
Examples
t=runif(10,min=0,max=1)
rSCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Sine-Log-logistic (SLL) Hazard Function.
Description
Sine-Log-logistic (SLL) Hazard Function.
Usage
rSLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the SLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L. (2015). New trigonometric classes of probabilistic distributions. esis, Universidade Federal Rural de Pernambuco, Brazil.
Examples
t=runif(10,min=0,max=1)
rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Tangent-Log-logistic (TLL) Hazard Function.
Description
Tangent-Log-logistic (TLL) Hazard Function.
Usage
rTLL(t, alpha, beta, log = FALSE)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the TLL hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Muse, A. H., Tolba, A. H., Fayad, E., Abu Ali, O. A., Nagy, M., & Yusuf, M. (2021). Modelling the COVID-19 mortality rate with a new versatile modification of the log-logistic distribution. Computational Intelligence and Neuroscience, 2021.
Examples
t=runif(10,min=0,max=1)
rTLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Weibull (W) Hazard Function.
Description
Weibull (W) Hazard Function.
Usage
rW(t, kappa, alpha, log = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
Value
the value of the w hazard function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
rW(t=t, kappa=0.75, alpha=0.5,log=FALSE)
Arcsine-Log-logistic (ASLL) Survival Function.
Description
Arcsine-Log-logistic (ASLL) Survival Function.
Usage
sASLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the ASLL Survival Function.
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
Examples
t=runif(10,min=0,max=1)
sASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Survivor Function.
Description
Arctangent-Log-logistic (ATLL) Survivor Function.
Usage
sATLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the ATLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions: Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
Examples
t=runif(10,min=0,max=1)
sATLL(t=t, alpha=0.7, beta=0.5)
Cosine-Log-logistic (CLL) Survivor Function.
Description
Cosine-Log-logistic (CLL) Survivor Function.
Usage
sCLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the CLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Mahmood, Z., M Jawa, T., Sayed-Ahmed, N., Khalil, E. M., Muse, A. H., & Tolba, A. H. (2022). An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics and Applications with Simulation Study. Mathematical Problems in Engineering, 2022.
Examples
t=runif(10,min=0,max=1)
sCLL(t=t, alpha=0.7, beta=0.5)
Exponentiated Weibull (EW) Survivor Function.
Description
Exponentiated Weibull (EW) Survivor Function.
Usage
sEW(t, lambda, kappa, alpha)
Arguments
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
Value
the value of the EW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Rubio, F. J., Remontet, L., Jewell, N. P., & Belot, A. (2019). On a general structure for hazard-based regression models: an application to population-based cancer research. Statistical methods in medical research, 28(8), 2404-2417.
Examples
t=runif(10,min=0,max=1)
sEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)
Gamma (G) Survivor Function.
Description
Gamma (G) Survivor Function.
Usage
sG(t, shape, scale)
Arguments
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
Value
the value of the G Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sG(t=t, shape=0.85, scale=0.5)
Generalised Gamma (GG) Survival Function.
Description
Generalised Gamma (GG) Survival Function.
Usage
sGG(t, kappa, alpha, eta, log.p = FALSE)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
Value
the value of the GG survival function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
Generalized Log-logistic (GLL) survivor function.
Description
Generalized Log-logistic (GLL) survivor function.
Usage
sGLL(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the GLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Muse, A. H., Mwalili, S., Ngesa, O., Alshanbari, H. M., Khosa, S. K., & Hussam, E. (2022). Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients. Alexandria Engineering Journal, 61(10), 7953-7978.
Examples
t=runif(10,min=0,max=1)
sGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Log-logistic (LL) Survivor Function.
Description
Log-logistic (LL) Survivor Function.
Usage
sLL(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
Value
the value of the LL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Survivor Hazard Function.
Description
Lognormal (LN) Survivor Hazard Function.
Usage
sLN(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
Value
the value of the LN Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sLN(t=t, kappa=0.75, alpha=0.95)
Modified Kumaraswamy Weibull (MKW) Survivor Function.
Description
Modified Kumaraswamy Weibull (MKW) Survivor Function.
Usage
sMKW(t, alpha, kappa, eta)
Arguments
t |
: positive argument |
alpha |
: Inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
Value
the value of the MKW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
Modified Log-logistic (MLL) survivor function.
Description
Modified Log-logistic (MLL) survivor function.
Usage
sMLL(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the MLL survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model. Applied Bionics and Biomechanics, 2022.
Examples
t=runif(10,min=0,max=1)
sMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
Power Generalised Weibull (PGW) survivor function.
Description
Power Generalised Weibull (PGW) survivor function.
Usage
sPGW(t, kappa, alpha, eta)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
Value
the value of the PGW survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival data. Statistics in Medicine, 40(19), 4213-4229.
Examples
t=runif(10,min=0,max=1)
sPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
Secant-log-logistic (SCLL) Survivor Function.
Description
Secant-log-logistic (SCLL) Survivor Function.
Usage
sSCLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the SCLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sSCLL(t=t, alpha=0.7, beta=0.5)
Sine-Log-logistic (SLL) Survivor Function.
Description
Sine-Log-logistic (SLL) Survivor Function.
Usage
sSLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the SLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
References
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the Sin-G class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3), 357-379.
Examples
t=runif(10,min=0,max=1)
sSLL(t=t, alpha=0.7, beta=0.5)
Tangent-Log-logistic (TLL) Survivor Function.
Description
Tangent-Log-logistic (TLL) Survivor Function.
Usage
sTLL(t, alpha, beta)
Arguments
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
Value
the value of the TLL Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sTLL(t=t, alpha=0.7, beta=0.5)
Weibull (W) Survivor Function.
Description
Weibull (W) Survivor Function.
Usage
sW(t, kappa, alpha)
Arguments
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
Value
the value of the W Survivor function
Author(s)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau abdisalam.hassan@amoud.edu.so
Examples
t=runif(10,min=0,max=1)
sW(t=t, kappa=0.75, alpha=0.5)