Improved likelihood inference for the shape parameter in Weibull regression

Efficient Estimation of the Weibull Shape Parameter Based on a Modified Profile Likelihood

The maximum likelihood estimator of the Weibull shape parameter can be very biased. An estimator based on the modified profile likelihood is proposed and its properties are studied. It is shown that the new estimator is almost unbiased with relative bias being less than 1% in most of situations, and it is much more efficient than the regular MLE. The smaller the sample or the heavier of the cen...

Analytical bounds for the MLE of the Weibull shape parameter

Inference on Overlap Coefficients under the Weibull Distribution: Equal Shape Parameter

In this paper we consider three measures of overlap, namelyMatusia’s measure ρ, Morisita’s measure λ and Weitzman’s measure∆. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible lif...

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

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. I...

Monitoring the Weibull Shape Parameter with Type II Censored Data

In this article, we introduce a method for monitoring the Weibull shape parameter β with type II (failure) censored data. The control limits depend on the sample size, the number of censored observations, the target average run length, and the stable value of β. The method assumes that the scale parameter α is constant during each sampling period, which is true under rational subgrouping. The p...