Approximate Bayes Estimators of the Logistic Distribution Parameters Based on Progressive Type-II Censoring Scheme

Mohamed Mahmoud Mohamed,Mohammed Yusuf Abdelaziz,Ahmed Rashad Moussa

doi:10.18187/pjsor.v12i3.1176

Mohamed Mahmoud Mohamed, Mohammed Yusuf Abdelaziz + Show 1 more

Open Access

https://doi.org/10.18187/pjsor.v12i3.1176

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Abstract

In this paper we develop approximate Bayes estimators of the parameters, reliability, and hazard rate functions of the Logistic distribution by using Lindley’s approximation, based on progressively type-II censoring samples. Noninformative prior distributions are used for the parameters. Quadratic, linex and general Entropy loss functions are used. The statistical performances of the Bayes estimates relative to quadratic, linex and general entropy loss functions are compared to those of the maximum likelihood based on simulation study.

Highlights

The logistic function is one of the most popular and widely used for growth models in demographic studies and proposed by Verhulst (1838-1845) see Balakrishnan (1992)
The normal distribution resembles to logistic distribution in shape but the logistic distribution has thicker tails and higher kurtosis than the normal distribution
The logistic distribution has been applied in studies of population growth, physicochemical phenomena, bio-assay and a life test data, see Balakrishnan (1992), and of biochemical data by Gupta et al (1967)

Summary

Introduction

The logistic function is one of the most popular and widely used for growth models in demographic studies and proposed by Verhulst (1838-1845) see Balakrishnan (1992). Progressive Type-II censoring scheme can be described as follows: Suppose n units are placed on a life test and the experimenter decides before hand the quantity m , the number of failures to be observed. At the time of the first failure, R1 of the remaining n 1 surviving units are randomly removed from the experiment. At the time of the second failure, R2 of the remaining n R1 2 units are randomly removed from the experiment. Assume the failure time distribution to be the logistic distribution with probability density function (pdf) x. The solution of the non-linear equations (2.5) is ˆ , ˆ

Bayes Estimates for the Unknown Parameters and

Simulation Studies

Concluding remarks