E-Bayesian Estimation for Rayleigh Model Using Progressive Type-II Censoring Data

Abstract

This article deals with using E-Bayesian method under progressively type-II censored sample from the Rayleigh distribution (RD) for computing the estimates of the parameter. The Bayesian and E-Bayesian estimators are obtained under squared error and LINEX loss functions. A comparison between E-Bayesian method and corresponding Bayes and maximum likelihood methods is presented using the Monte Carlo simulation study.

Estimations in a Constant‐Stress Partially Accelerated Life Test for Generalized Rayleigh Distribution under Type‐II Hybrid Censoring Scheme

“…where 􏽢 λ B (a 1 , b 1 ) and 􏽢 θ B (a 2 , b 2 ) stand for Bayesian estimated values of λ and θ under the effect of both SEL function and the LINEX loss function. For further information, we refer to [13][14][15][16][17][18][19][20][21][22][23][24].…”

E‐Bayesian estimation for the parameters and hazard function of Gompertz distribution based on progressively type‐II right censoring with application

“…Then, the E‐BE of α (expectation of the BE of α) can be written as $$$$\begin{equation}{\hat{\alpha }}_{E - B} = \int\!\!\!\int {\hat{\alpha }}_B\left( {a,b} \right){{\pi}}\left( {{\rm{a}},{\rm{b}}} \right)dadb,\ \end{equation}$$$$where $${\hat{\alpha }}_B( {a,b} )$$ is the BE of α under SEL, ALB and LINEX loss functions, given by Equations (), (), and (), respectively. For elaboration, see El‐Sagheer 2 …”

“…For elaboration, see El-Sagheer. 2 In this section we study the E-BE for the parameter 𝛼 based on three different distributions of the hyper parameters 𝑎 and 𝑏. The first and the second distributions are introduced by Han, 1 while we suggest the third distribution 𝜋 3 (𝑎, 𝑏).…”

“…Hence to overcome those difficulties E‐BE method of failure rate was introduced by Han 1 . EL‐Sagheer 2 derived E‐BE for Rayleigh distribution using PTIIRCOS data. Jaheen and Okasha 3 derived E‐BE for the Burr type XII distribution based on Type‐II censoring.…”

Prediction for Modified Topp Leone-Chen Distribution Based on Progressive Type-II Censoring Scheme

“…Han [11] introduced the expected Bayesian (E-Bayesian) estimation method which is very simple and it's a special Bayesian method used in the area related for the life testing of products with high reliability, small sample size or censored data. Many researchers applied the E-Bayesian method to many distributions, such as, Okasha [12], Azimi et al [13], Okasha [14], Reyad and Ahmed [15], Reyad and Ahmed [16], Nasiri and Esfandyarifar [17], Reyad et al [18], EL-Sagheer [19], Shawky and Al-Aboud [20], Reyad et al [21], Reyad and Othman [22], Han [23], Okasha [24], Rabie and Li [25], Algarni et al [26], Han [27], Piriaei et al [28] and Rabie and Li [29].…”