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

Abstract

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