Inequalities involving expectations to characterize distributions

The characterization of distributions is well known in the field of Statistics and Reliability. This paper characterizes a few distributions with the help of failure rate, mean residual, log-odds rate, and aging intensity functions.

[1]  J. Ord,et al.  Characterization Problems in Mathematical Statistics , 1975 .

[2]  Ganapati P. Patil,et al.  Statistical Distributions in Scientific Work , 1981 .

[3]  S. Alam,et al.  Properties of aging intensity function , 2007 .

[4]  A. G. Laurent.  On Characterization of Some Distributions by Truncation Properties , 1974 .

[5]  R. Jiang,et al.  Aging property of unimodal failure rate models , 2003, Reliab. Eng. Syst. Saf..

[6]  A. K. Nanda.  Characterization of distributions through failure rate and mean residual life functions , 2010 .

[7]  Log-odds rate and monotone log-odds rate distributions , 1998 .

[8]  Estimation using the modified profile likelihood in log odds ratio regression analysis , 1998 .

[9]  Toji Makino.  Mean hazard rate and its application to the normal approximation of the weibull distribution , 1984 .

[10]  J. Galambos.  Characterizations of Probability Distributions by Properties of Order Statistics I , 1975 .

[11]  J. C. Helton.  The engineering statistician's guide to continuous bivariate distributions: T.P. Hutchinson and C.D. Lai. Rumsby Scientific Publishing, Adelaide, Australia, 1991. ISBN-0-646-02413-2 , 1993 .

[12]  S. Sunoj,et al.  Characterizations of distributions using log odds rate , 2007 .

[13]  William J. Zimmer,et al.  Monotone Log-Odds Rate Distributions in Reliability Analysis , 2003 .

[14]  S. Kotz.  Characterizations of Statistical Distributions: a Supplement to Recent Surveys , 1974 .

[15]  New estimators of discriminant coefficients as the gradient of log-odds , 2004 .

[16]  On linear lon-odds and estimation of discriminant coefficients , 1986 .

[17]  Wilson Confidence Intervals for the Two-Sample Log-Odds-Ratio in Stratified 2 × 2 Contingency Tables , 2012 .

[18]  Characterizations and ordering properties based on log-odds functions , 2008 .