Inference for the Weibull Distribution: A tutorial

Abstract

This tutorial deals with the 2-parameter Weibull distribution. In particular it covers the construction of confidence bounds and intervals for various parameters of interest, the Weibull scale and shape parameters, its quantiles and tail probabilities. These bounds were pioniered in Thoman, Bain, and Antle, 1969, Thoman, Bain, and Antle, 1970, Bain, 1978, and Bain and Engelhardt, 1991, where tables for their computation were given. These tables were based on simulations and show occasional irregularities. In conjunction with this tutorial we provide R code to perform various tasks (generating plots, performsimulations). It greatly simplifies the application of thesemethods over trying to use the tables available so far. Today’s computing availability and speed makes this very viable. For the freely available R computing platformwe refer to R Core Team, 2015. The text identifies R code by using courier font in appropriate places.

Keywords

• Weibull distribution
• confidence intervals
• Inference
• R