Comparing the Shape Parameters of Two Weibull Distributions Using Records: A Generalized Inference

TL;DR

This paper introduces a new statistical method for comparing the shape parameters of two Weibull distributions using record data, filling a gap in existing inference techniques.

Contribution

It proposes a generalized p-value and confidence interval approach for hypothesis testing and estimation of shape parameter ratios and differences.

Findings

Method performs satisfactorily in simulations

Provides confidence intervals and hypothesis tests

Illustrated with a real data example

Abstract

The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an appropriate method for comparing the shape parameters in the literature. Therefore, comparing the shape parameters of two Weibull distributions is very important. In this paper, we propose a method for constructing confidence interval and testing hypotheses about the ratio and difference of shape parameters using the concept of the generalized {\it p}-value and the generalized confidence interval. Simulation studies showed that our method is satisfactory. In the end, a real example is proposed to illustrate this method.