Derivation of a Class of Frequency Distributions Via Bayes's Theorem
Carl‐Erik Särndal · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1965
Summary Being in some respects expository in character, this paper uses Bayes's theorem to derive a k-variate discrete probability distribution which is fundamental inasmuch as it proliferates, under various sets of asymptotic conditions, to yield as its limiting forms an array of other k-variate distributions including the multinomial, independent Poisson, independent negative binomial, independent gamma, Dirichlet and multivariate normal. A systematic arrangement of these distributions thereby suggests itself, and a number of properties pertaining to the distributions are discussed within the framework created by this arrangement.