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Biometrika 1995 82(2):437-438; doi:10.1093/biomet/82.2.437
© 1995 by Biometrika Trust
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MISCELLANEA

A note on smooth tests of goodness of fit for location-scale families

BERNARD BOULERICE and GILLES R. DUCHARME

Département de mathématiques et statistique, Université de Montréal C.P. 6128, Succ. "Centre-Ville", Montréal, Québec, Canada, H3C 3J7
Laboratoire de probabilités et statistique, Département des sciences mathématiques, cc050, Université Montpellier II Place Eugéne Bataillon, 34095, Montpellier Cedex 5, France

In this note, we show that the test statistic given by Rayner & Best (1986) for Neyman's (1937) smooth test of goodness of fit for location-scale families does not, in general, have the alleged chi-squared distribution. As a result, gross error may result from using their test strategy. The size of this error is obtained for the logistic distribution.

Key Words: Goodness of fit • Location-scale family • Logistic distribution • Orthonormal polynomials • Smooth test


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