Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 2, 249--258

Characterizations Of The Exponential Distribution Via The Residual Lifetime


GWO DONG LIN, Academia Sinica, Taiwan

SUMMARY. This paper clarifies and extends significantly Chong's (1977)  characterization result in terms of the residual lifetime. In particular, let $X$ be a positive random variable with finite mean and denote the mean residual lifetime (MRL)  $h(x)=E(\hbox{max}\{X-x,0\})$. Then we prove that if the square of the MRL $h(x)$ is proportional to $h(2x)$, $X$ is exponentially distributed. Secondly, a general result concerning the higher-order moments of the residual lifetime is given. Finally, the exponential distribution is characterized by a new relation of its moments.

AMS (1991) subject classification. 60E05, 62E10.

Key words and phrases. Exponential distribution, residual lifetime, lack-of-memory property.

Full paper (PDF)