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Goodness‐of‐fit testing of a weak memoryless property of life distributions
Author(s) -
Ahmad Ibrahim A.,
Alwasel Ibrahim A.
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00344.x
Subject(s) - mathematics , goodness of fit , test statistic , quantile , statistics , property (philosophy) , empirical distribution function , statistic , conditional probability distribution , statistical hypothesis testing , philosophy , epistemology
Summary A life distribution is said to have a weak memoryless property if its conditional probability of survival beyond a fixed time point is equal to its (unconditional) survival probability at that point. Goodness‐of‐fit testing of this notion is proposed in the current investigation, both when the fixed time point is known and when it is unknown but estimable from the data. The limiting behaviour of the proposed test statistic is obtained and the null variance is explicitly given. The empirical power of the test is evaluated for a commonly known alternative using Monte Carlo methods, showing that the test performs well. The case when the fixed time point t 0 equals a quantile of the distribution F gives a distribution‐free test procedure. The procedure works even if t 0 is unknown but is estimable.