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 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 pro- posed. 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.

Keywords

• Cramer-von Mises Statistics; Exponential model; Goodness of fit test; Kolmogorov-Smirnov statis- tics; Likelihood ratio test; Record data; Weibull model.