Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Shi, Xiaolin; Shi, Yimin; Zhou, Kuang

doi:10.3390/e23020206

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…Bantan et al [18] discussed the estimation of entropy for the inverse Lomax distribution under multiple censoring data. Shi et al [19] discussed the estimation of entropy for the generalized Bilal distribution under adaptive Type-II hybrid censored data and obtained ML estimates of entropy and parameters using Newton's iteration method. Liu and Gui [20] discussed the estimation problem of entropy for the two-parameter Lomax distribution under generalized asymptotic hybrid censored data.…”

Section: Shannon Entropy Of Grd(σ β)mentioning

confidence: 99%

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Ren

Gong

Han

2023

Axioms

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This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations.

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Section: Shannon Entropy Of Grd(σ β)mentioning

confidence: 99%

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Ren

Gong

Han

2023

Axioms

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“…In addition, Yu et al [7] considered ML and Bayesian methods on the Shannon entropy of inverse Weibull distribution under the PFFC. Furthermore, Shi et al [21] attained estimation for entropy and parameters of generalized Bilal distribution under an adaptive Type II progressive hybrid censoring scheme. In this paper, we presume the prior distribution of unknown parameters in order to examine the Bayes estimators.…”

Section: Asymptotic Confidence Interval (Aci) For Entropymentioning

confidence: 99%

Bayesian Estimation of Entropy for Kumaraswamy Distribution and Its Application to Progressively First-Failure Censored Data

Modhesh

Basheer²

2023

AJPAS

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Entropy can be mathematically defined as a measure of the uncertainty of random variables that represents the potential quantity of information. This article investigates the behavior of the entropy of random variables which follow a Kumaraswamy distribution using progressively first-failure censored (PFFC) data. In particular, we calculate the maximum likelihood estimation and the confidence interval of entropy by using the observed Fisher information matrix through the asymptotic distribution of the maximum likelihood estimator. Furthermore, we apply the Markov Chain Monte Carlo (MCMC) method which help us to estimates the entropy and to formulation the credible intervals in order to address this problem. Here, a numerical example of real data is presented to illustrate the performance of the proposed method. Finally, we perform Monte Carlo simulations to observe the behavior of the proposed procedure.

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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 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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Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Cited by 8 publications

References 33 publications

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Bayesian Estimation of Entropy for Kumaraswamy Distribution and Its Application to Progressively First-Failure Censored Data

Discrete Bilal distribution with right-censored data

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