Poisson distributions: Identification of parameters from the distribution of the maximum and a conjecture on the partial sums of the power series for exp(x)

L. Bi and A. Mukherjea

Statistics & Probability Letters, 2011, vol. 81, issue 5, 611-613

Abstract: Let (X1,X2,...,Xn) be n independent Poisson (real) random variables with (positive) parameters [lambda]1,[lambda]2,...,[lambda]n respectively. Then does the distribution of the maximum of the X(i)s determine uniquely the parameters [lambda]i? This is the question that we discuss in this note. This question brings up an interesting, probably difficult, conjecture involving the partial sums of the power series for exp(x). A similar conjecture comes up in the context of the corresponding minimum problem.

Keywords: Poisson; distributions; Identification; of; the; parameters; The; distribution; of; the; maximum (search for similar items in EconPapers)
Date: 2011
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