On the Maximum Likelihood and Least Squares Estimation for the Inverse Weibull Parameters with Progressively First-Failure Censoring

Amal Helu

doi:10.4236/ojs.2015.51010

Abstract

In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.

Highlights

Let T follow ( )a two-parameter Weibull distribution (α, β ) with the probability density function = f (t;α, β ) β α t α β −1 e−(α t )− β, t>0How to cite this paper: Helu, A. (2015) On the Maximum Likelihood and Least Squares Estimation for the Inverse Weibull Parameters with Progressively First-Failure Censoring
We have considered the maximum likelihood estimates (MLE), approximate MLE and least square estimators (LSE) to estimate the unknown parameters of the IW distribution when data under consideration are progressively first-failure censoring
It is out of question that all estimates are affected by the choice of k, and our goal is to compare the three methods namely MLE, approximate values for the maximum likelihood estimators (AMLE) and LSE and decide which is the most efficient for estimating α and β

Summary

Introduction

A two-parameter Weibull distribution (α , β ) with the probability density function (pdf) = f (t;α, β ) β α t α β −1 e−(α t )− β , t>0. (2015) On the Maximum Likelihood and Least Squares Estimation for the Inverse Weibull Parameters with Progressively First-Failure Censoring. A. Helu X = 1 has an (IW) distribution with pdf T.

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