Incomplete moments of the inverse Pólya distribution

Tadeusz Gerstenkorn, and Joanna Jarzębska. "Incomplete moments of the inverse Pólya distribution." Mathematica Applicanda 10.20 (1982): null. <http://eudml.org/doc/293051>.

@article{TadeuszGerstenkorn1982,
abstract = {The authors continue the study of incomplete moments of discrete distributions by Gerstenkorn [Rev. Roumaine Math. Pures Appl. 26 (1981), no. 3, 405–416; MR0627288; Bull. Inst. Internat. Statist. 46 (1975), no. 3, 290–297; MR0471020]. For a discrete nonnegative random variable X, the left incomplete factorial moment of order l truncated at s is defined by ∑sx=0x(x−1)⋯(x−(l−1))P(X=x). The authors evaluate the left incomplete factorial moments of the inverse Polya distribution (Theorem 1). From this result they derive the complete factorial moments and recurrence relations between incomplete and complete factorial moments as well as between incomplete factorial moments of different orders. These results are demonstrated for special inverse Polya distributions: the inverse Polya distribution connected with Polya trials, the negative binomial distribution, the inverse hypergeometric distribution, and the geometric distribution. MR0707818},
author = {Tadeusz Gerstenkorn, Joanna Jarzębska},
journal = {Mathematica Applicanda},
keywords = {Exact distribution theory},
language = {eng},
number = {20},
pages = {null},
title = {Incomplete moments of the inverse Pólya distribution},
url = {http://eudml.org/doc/293051},
volume = {10},
year = {1982},
}

TY - JOUR
AU - Tadeusz Gerstenkorn
AU - Joanna Jarzębska
TI - Incomplete moments of the inverse Pólya distribution
JO - Mathematica Applicanda
PY - 1982
VL - 10
IS - 20
SP - null
AB - The authors continue the study of incomplete moments of discrete distributions by Gerstenkorn [Rev. Roumaine Math. Pures Appl. 26 (1981), no. 3, 405–416; MR0627288; Bull. Inst. Internat. Statist. 46 (1975), no. 3, 290–297; MR0471020]. For a discrete nonnegative random variable X, the left incomplete factorial moment of order l truncated at s is defined by ∑sx=0x(x−1)⋯(x−(l−1))P(X=x). The authors evaluate the left incomplete factorial moments of the inverse Polya distribution (Theorem 1). From this result they derive the complete factorial moments and recurrence relations between incomplete and complete factorial moments as well as between incomplete factorial moments of different orders. These results are demonstrated for special inverse Polya distributions: the inverse Polya distribution connected with Polya trials, the negative binomial distribution, the inverse hypergeometric distribution, and the geometric distribution. MR0707818
LA - eng
KW - Exact distribution theory
UR - http://eudml.org/doc/293051
ER -