A Characteristic Property of Certain Generalized Power Series Distributions
There are some probability distributions which remain invariant in their form under suitable transformations. In this paper, we show that the logarithmic series distribution and the geometric distribution enjoy the property of invariance of form as a characterizing property under a special type of transformation which we introduce below as a modulo sequence. Further, we provide a necessary and sufficient condition for the generalized power series distribution to have this characteristic property.
Key WordsModulo sequence logarithmic series distribution geometric distribution
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