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- W2494961418 abstract "SUMMAR Y. The Stirling numbers of the first and second kind and the C numbers appear ing in the n-fold convolution of the logarithmic series, the Poisson and the binomial distri butions truncated at zero, respectively, are generalized using a suitable exponential generating function in each case. Recurrence relations, useful for tabulation purposes, are given for these generalized numbers. Moreover, some applications of these numbers to combinatorial analysis are also, provided. distribution of the sufficient statistic, that is of the sum Z = 2 X< of the ?=i observations when the truncation point is known and of (Y, Z), where Y = min{Xl5 ..., Xn}, when the truncation point is unknown, led to the intro duction of the generalized Stirling numbers of the first kind in the logarithmic series case, of the second kind in the Poisson case and of the generalized C numbers in the binomial and negative binomial cases. This generalization is based on a suitable exponential generating function in each case as suggested by the corresponding generating function of the usual Stirling and G numbers which solve the problem when the truncation is only at zero (see Section 3 below). It should be noted that the relations between these generalized numbers, as shown below, reflect the intrinsic relations between the Poisson and the binomial and negative binomial distributions. In addition to their statistical applications, these numbers are shown to be useful in the solution of several problems of combinatorial analysis." @default.
- W2494961418 created "2016-08-23" @default.
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- W2494961418 date "2016-01-01" @default.
- W2494961418 modified "2023-09-27" @default.
- W2494961418 title "THE GENERALIZED STIRLING AND C NUMBERS" @default.
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- W2494961418 hasPublicationYear "2016" @default.
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