Goodness-of-fit tests for weibull populations on the basis of records

TL;DR

This paper develops and evaluates new goodness-of-fit tests for Weibull distributions using record data, including Kolmogorov-Smirnov, Cramer-von Mises, and a novel weighted test, supported by simulations and real data analysis.

Contribution

It introduces new goodness-of-fit tests for Weibull models based on record data, filling a gap in model checking methods for such data types.

Findings

Proposed Kolmogorov-Smirnov and Cramer-von Mises tests for Weibull records.

Developed a new weighted goodness-of-fit test.

Simulation study to determine critical values and real data applications.

Abstract

Record is used to reduce the time and cost of running experiments (Doostparast and Balakrishnan, 2010). It is important to check the adequacy of models upon which inferences or actions are based (Lawless, 2003, Chapter 10, p. 465). In the area of goodness of fit based on record data, there are a few works. Smith (1988) proposed a form of residual for testing some parametric models. But in most cases, the variation inherent in graphical summaries is substantial, even when the data are generated by assumed model, and the eye can not always determine whether features in a plot are within the bounds of natural random variation. Consequently, formal hypothesis tests are an important part of model checking (Lawless, 2003). In this paper, Kolmogorov-Smirnov and Cramer-von Mises type goodness of fit tests for record data are proposed. Also a new weighted goodness of fit test is suggested. A Monte-Carlo simulation study is conducted to derive the percentiles of the statistics proposed. Finally, some real data sets are given to investigate results obtained.