Tests of fit for exponentiality based on a characterization via the mean residual life function

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GOODNESS-OF-FIT TESTS BASED ON A NEW CHARACTERIZATION OF THE EXPONENTIAL DISTRIBUTION (2002, background): “(3.1) is equivalent to the condition E½minðX , tÞ ¼ FðtÞ for each t > 0, Baringhaus and Henze[12] suggested the Kolmogorov–Smirnov type statistic KSn ¼ ffiffiffi n p sup t 0 1n Xn j¼1 minðYj, tÞ 1 n Xn j¼1 1fYj tg and the Cramér-von Mises type statistic CMn ¼ n Z 1 0 1 n Xn j¼1 minðYj, tÞ 1 n Xn j¼”
Recent and classical tests for exponentiality: a partial review with comparisons (2005, methodology): “Since this condition is equivalent to E ½minðX ; tÞ ¼ l F ðtÞ for each t > 0, Baringhaus and Henze (2000) suggested the Kolmogorov-Smirnov type statistic KSn ¼ ffiffiffi n p sup t 0 1 n Xn j¼1 minðYj; tÞ 1 n Xn j¼1 1fYj tg ¼ ffiffiffi n p maxðKSþn ;KS n Þ; where KSþn ¼ maxj¼0;1;...”