Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 2, 267--272

A NOTE ON THE L-CLASS OF LIFE DISTRIBUTIONS

By

GWO DONG LIN, Academia Sinica, Taipei

and

CHIN-YUAN HU, National Changhua University of Education, Changhua

SUMMARY. We first amend Klefsj\"o's (1983) proof for the result that the L-class of life distributions is strictly larger than the HNBUE class (the harmonic new better than used in expectation class). By a simpler proof, Chaudhuri, Deshpande and Dharmadhikari's (1996) functional bound for life distributions is extended from the case of L-class to the case of L-like class. We take a different approach to prove the finiteness of the second moment of distributions F in the L-like classes. This approach enables us to obtain a more general result. Finally, the preservation of the L-class of life distributions under geometric compounding is investigated.

AMS (1991) subject classification. Primary 62E10, 44A10.

Key words and phrases. L-class; L-like class; HNBUE class; Laplace-Stieltjes transform; coefficient of variation; bound of distribution; geometric compounding.

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