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

Author:
,
Year
: 2015
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.
Keyword(s): Cramer-von Mises Statistics,Exponential model,Goodness of fit test,Kolmogorov-Smirnov statistics,Likelihood ratio test,Record data,Weibull model
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