Compound and Mixture Distributions
Ch. A. Charalambides · Wiley series in probability and statistics · 2005
Under a random occupancy model, with a random number of urns and the number of balls distributed into any specific urn obeying a discrete probability law, the (compound) distribution of the total number of balls distributed into the urns is derived. A class of countable mixture discrete distributions, which is connected to the class of compound discrete distributions, is briefly discussed. Particular compound distributions, with Poisson, binomial, negative binomial and logarithmic compounding distributions, are examined. Also, the compound Poisson, logarithmic and negative binomial distributions are studied. Reference notes on the original contributions and a section with exercises and complements are included at the end of the chapter.