The graphical method for goodness of fit test in the inverse Weibull distribution based on multiply type-II censored samples.

Suk-Bok Kang,Jun-Tae Han

doi:10.1186/s40064-015-1554-x

Abstract

Many studies have considered a truncated and censored samples which are type-I, type-II and hybrid censoring scheme. The inverse Weibull distribution has been utilized for the analysis of life testing and reliability data. Also, this distribution is a very flexible distribution. The inverse Rayleigh distribution and inverse exponential distribution are a special case of the inverse Weibull distribution. In this paper, we derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also propose a simple graphical method for goodness-on-fit test based on multiply type-II censored samples using AMLEs.

Highlights

Fei et al (1995) studied the estimation for the two-parameter Weibull distribution and extreme-value distribution under multiply type-II censoring
The probability density function (PDF) and the cumulative distribution function (CDF) of the two-parameter inverse Weibull distribution are given by g(x; σ, ) = σ − x−( +1)exp −(xσ )−, x > 0, σ > 0, > 0 (1.1)
We propose a simple graphical method for goodness-of-fit test based on multiply type-II censored samples using approxi‐ mate maximum likelihood estimators (AMLEs)

Summary

Introduction

Fei et al (1995) studied the estimation for the two-parameter Weibull distribution and extreme-value distribution under multiply type-II censoring. Shimokawa and Liao (1999) studied the goodness of fit test for the extreme value and Weibull distribution, when the population parameters are estimated from a complete sample by graphical plotting techniques. We propose a simple graphical method for goodness-of-fit test based on multiply type-II censored samples using AMLEs. The paper is organized as follows.

Results

Conclusion