E-Bayesian estimations for the cumulative hazard rate and mean residual life based on exponential distribution and record data

Piriaei, Hassan; Yari, Gholamhossein; Farnoosh, Rahman

doi:10.1080/00949655.2019.1678623

Cited by 11 publications

(3 citation statements)

References 26 publications

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“…Reference [20] obtained the E-Bayesian estimation of Burr Type-XII distribution using adaptive progressive Type-II censored data. Reference [21] studied the E-Bayesian estimations for the exponential distribution based on record data. Reference [11] considered the E-Bayesian estimations for some lifetime parameters of the GIED using Type-II censoring.…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

2022

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The E-Bayesian estimation approach has been presented for estimating the parameter and/or reliability characteristics of various models. Several investigations in the literature have considered this method under the assumption that just one parameter is unknown. So, based on Type-II censoring, this study proposes for the first time an effort to use the E-Bayesian estimation approach to estimate the full model parameters as well as certain related functions such as the reliability and hazard rate functions. To illustrate this purpose, we apply the proposed technique to the two-parameter generalized inverted exponential distribution which can be considered to be one of the most flexible asymmetrical probability distributions. Moreover, the E-Bayesian method, maximum likelihood, and Bayesian estimation approaches are also considered for comparison purposes. Under the assumption of independent gamma priors, the Bayes and E-Bayes estimators are developed using the symmetrical squared error loss function. Due to the complex form of the joint posterior density, two approximation techniques, namely the Lindley and Markov chain Monte Carlo methods, are considered to carry out the Bayes and E-Bayes estimates and also to construct the associate credible intervals. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To demonstrate the applicability of the proposed methods in real phenomenon, one real data set is analyzed and it shows that the proposed method is effective and easy to operate in a real-life scenario.

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Section: Introductionmentioning

confidence: 99%

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

2022

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“…For instance, they allow prediction of the possible time of earthquakes, floods, extreme weather events, and life-testing studies. Many scholars have researched record values and associated statistics, including generalized extreme value distribution [1], Lomax distribution [2], Weibull distribution [3]; Yang et al [4,5], lognormal distribution [6], ratio of Weibull random variables [7], power Lindley model [8], exponential distribution [9], generalized Rayleigh model [10], and inverse Weibull distribution (IWD) [11][12][13][14][15][16]. In this work, we will investigate IWD based on record values.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

Al-Duais

2021

Mathematical Problems in Engineering

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The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

AL-Dayian

EL-Helbawy

AL-Sayed

et al. 2021

JAMCS

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Prediction of future events on the basis of the past and present information is a fundamental problem of statistics, arising in many contexts and producing varied solutions. The predictor can be either a point or an interval predictor. This paper focuses on predicting the future observations from the modified Topp-Leone Chen distribution based on progressive Type-II censored scheme. The two-sample prediction is applied to obtain the maximum likelihood, Bayesian and E-Bayesian prediction (point and interval) for future order statistics. The Bayesian and E-Bayesian predictors are considered based on two different loss functions, the balanced squared error loss function; as a symmetric loss function and balanced linear exponential loss function; as an asymmetric loss function. The predictors are obtained based on conjugate gamma prior and uniform hyperprior distributions. A numerical example is provided to illustrate the theoretical results and an application using real data sets are used to demonstrate how the results can be used in practice.

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E-Bayesian estimations for the cumulative hazard rate and mean residual life based on exponential distribution and record data

Cited by 11 publications

References 26 publications

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

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

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