Abstract
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.
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Ahmed, A.N., Abouammoh, A.M. Characterizations of gamma, inverse Gaussian, and negative binomial distributions via their length-biased distributions. Statistical Papers 34, 167–173 (1993). https://doi.org/10.1007/BF02925538
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DOI: https://doi.org/10.1007/BF02925538