A general form for characterizing inverse Gaussian and Wald distributions, based on their respective length-biased distributions, is introduced. Further results for characterizations of the gamma distribution, the negative binomial distribution and some mixtures of them by using their lengthbiased distributions are establised.
Length biased distribution Negative binomial distribution Gamma distribution Inverse Gaussain distribution Chi-square distribution Mixed distributions
This is a preview of subscription content, log in to check access
Gupta, R. and Keating, J. (1986). Relations for reliability measures under length-biased sampling. Scandinavian Journal of statistics 13, ppl 49–56.MathSciNetGoogle Scholar
Khattree, R. (1989). Characterization of inverse-Gaussian and Gamma distributions through their length-biased distributions. IEEE. Trans. on Reliability, Vol. 38, No. 5, pp. 610–611.MATHCrossRefGoogle Scholar
Patil, P. and Rao, R. (1977). The weighted distributions: A survey of their applications. In Applications in Statistics (ed. Krishnaiah, R.). North Holland, pp. 383–405.Google Scholar
Ross, S. (1983). Stochastic Processes. John Wiley & Sons, Inc., New York.MATHGoogle Scholar