Abstract
Goodness-of-fit (GOF) techniques are used for assessment whether a distribution is suitable to describe a data set or not. These techniques have been studied for distributions belonging to the location-scale family. However, one could be interested in making this assessment for distributions that do not belong to this family. We review the available GOF tests and propose graphical tools based on these tests for censored and uncensored data from non-location-scale distributions. Anderson-Darling, Cramer-von Mises, Kolmogorov-Smirnov, Kuiper, Michael and Watson GOF statistics are considered. We apply the proposed results to real-world data sets to illustrate their potential, with emphasis on some Birnbaum-Saunders distributions.
Highlights
Life distributions are widely studied and applied; see Lawless (2003) and Marshall & Olkin (2007)
We reviewed goodness-of-fit tests for life distributions not belonging to the location-scale family with uncensored and type-II right censored data
We considered the most used tests to assess goodness-of-fit based on the empirical distribution function
Summary
Life distributions are widely studied and applied; see Lawless (2003) and Marshall & Olkin (2007). Ordered observations corresponding to empirical quantiles can be plotted versus the theoretical quantiles of a specified distribution in a graph known as the QQ plot; see Marden (2004) This author studied such a plot in the case of the normal distribution and provided tools for graphical comparison of two samples, extending the QQ plot to multivariate data. The graph related to this variance stabilizing transformation is known as the stabilized probability (SP) plot and the statistic associated with the test proposed by Michael (1983) is denoted as MI This author studied the power of the MI test showing that it proves more powerful than the KS test for certain alternative hypotheses.
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