Approximate Bayes estimators applied to the Bilal model

Abd-Elrahman, Ayman M.; Niazi, Sherif F.

doi:10.1016/j.joems.2016.05.001

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…# Reading data (Wang et al, 2015) t <-c (3,7,11,18,22,25,28,32,34,35,35,36,40,40,41,54,66,76,84,88,92) d <-c(1,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0) n <-length(t) # the sample size K <-2 # number of parameters # Loading the maxLik package library(maxLik) # The likelihood function log.f <-function(parms…”

Section: Appendice: R Codesmentioning

confidence: 99%

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

Freitas

Achcar

Peres

et al. 2022

Stat., optim. inf. comput.

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The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction.

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Section: Appendice: R Codesmentioning

confidence: 99%

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

Freitas

Achcar

Peres

et al. 2022

Stat., optim. inf. comput.

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Section: Appendice: R Codesmentioning

confidence: 99%

Discrete Bilal distribution with right-censored data

Freitas¹,

Achcar²,

Peres³

et al. 2021

Preprint

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This paper presents inferences for the discrete Bilal (DB) distribution introduced by Altun et al. ( 2020). We consider parameter estimation for DB distribution in the presence of randomly right-censored data. We use maximum likelihood and Bayesian methods for the estimation of the model parameters. We also consider the inclusion of a cure fraction in the model. The usefulness of the proposed model was illustrated with three examples considering real datasets. These applications suggested that the model based on DB distribution performs at least as good as some other traditional discrete models as the DsFx-I, discrete Lindley, discrete Rayleigh, and discrete Burr-Hatke distributions. R codes are provided in an appendix at the end of the paper so that reader can carry out their own analysis.

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“…r is a type-II random sample from Bilal(θ) distribution. Abd-Elrahman and Niazi [7] established the existence and uniqueness theorem for the maximum likelihood estimate (MLE) of the parameter θ, sayθ M . The MLE for the parameter β is then bŷ β M λ (0) (0) exists and it is unique.…”

Section: When λ Is Knownmentioning

confidence: 99%

“…are as given by (7) after replacing β, λ (0) by β (0) and λ, respectively. In order to established the existence and uniqueness of the MLE for λ, the following theorem is needed.…”

Section: When β Is Knownmentioning

confidence: 99%

Reliability estimation under type-II censored data from the generalized Bilal distribution

Abd-Elrahman

2019

J Egypt Math Soc

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The main object of this article is the estimation of the unknown population parameters and the reliability function for the generalized Bilal model under type-II censored data. Both maximum likelihood and Bayesian estimates are considered. In the Bayesian framework, although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibb's sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute the Bayes estimates and also to construct their corresponding credible intervals with the help of two different importance sampling techniques. A simulation study is carried out to examine the accuracy of the resulting Bayesian estimates and compare them with their corresponding maximum likelihood estimates. Application to a real data set is considered for the sake of illustration.

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Approximate Bayes estimators applied to the Bilal model

Cited by 4 publications

References 10 publications

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

Discrete Bilal distribution with right-censored data

Reliability estimation under type-II censored data from the generalized Bilal distribution

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