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Estimation of the Quantile Function of an IFRA Distribution
Author(s) -
Rojo Javier
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00104
Subject(s) - mathematics , quantile , statistics , estimation , econometrics , distribution (mathematics) , function (biology) , mathematical analysis , evolutionary biology , biology , management , economics
Let F and G be lifetime distributions and consider the problem of estimating F −1 when it is known that G −1 F is star‐shaped. Estimators of F −1 are considered here which are shown to be uniformly strongly consistent. The case of censored data is also presented. Asymptotic confidence intervals and bands for F −1 are provided. The result are applicable, for example, to the estimation of quantile functions of k ‐out‐of‐ n systems in reliability. The special case of an IFRA distribution follows immediately from the more general case presented here