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Selecting a power‐series distribution for goodness of fit
Author(s) -
Wani Jagannath K.,
Lo HingPo
Publication year - 1986
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315193
Subject(s) - mathematics , negative binomial distribution , series (stratigraphy) , statistics , poisson distribution , logarithm , factorial , logarithmic distribution , binomial distribution , goodness of fit , negative multinomial distribution , range (aeronautics) , beta binomial distribution , power series , binomial (polynomial) , mathematical analysis , paleontology , materials science , composite material , biology
The binomial, Poisson, logarithmic, negative binomial, and extended negative binomial distributions are characterized in the class of power‐series distributions (1) through a differential equation based on the ratio of two successive derivatives of the series function, (2) through the ratio of two probabilities associated with two successive values in the range of the random variable, and (3) through the ratio of two consecutive factorial moments. The ratios referred to in (2) and (3) above can be utilized to discriminate between the five power‐series distributions mentioned at the beginning.