A new flexible class of omnibus tests for exponentiality
Titel:
A new flexible class of omnibus tests for exponentiality
Auteur:
Henze, Norbert
Verschenen in:
Communications in statistics
Paginering:
Jaargang 22 (1992) nr. 1 pagina's 115-133
Jaar:
1992
Inhoud:
Let X1,…,Xn be independent and identically distributed non-negative random variables, and let Yj = XjXn (j= 1,…,n), where [image omitted] If X1 has the exponential density λexp(-λx),x>0, for some λ>0, the empirical Laplace transform [image omitted] of Y1,…,Yn should be close to (1 + t)-1 which is the Laplace transform of the unit exponential distribution. We study the properties of [image omitted] as a statistic for testing for exponentiality. The limiting null distribution of Tn,a is found, and it is shown that the test rejecting the hypothesis of exponentiality for large values of Tn,a is consistent against each fixed alternative distribution. This new class of tests offers great flexibility in that the parameter a may be chosen so as to yield high power against specific alternatives. It is also possible to let a depend on X1,…, Xn. Power performance of the new tests for finite samples is assessed in a Monte Carlo study.
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