RI 6552 Some generalized probability distributionss

This report (the second in a series of five) presents the mathematical development in extending the theory of sample reliability from a sample consisting of a fixed number of items to a sample consisting of a fixed amount of items. Examples of a fixed amount of items per sample are samples consisting of a fixed weight or a fixed volume of unequal size particles. The probability distribution functions (those here called the compound binomial and compound multinomial functions) are developed from fundamentals. Their distributions are generalized to include some measured characteristic of the items. Infinite population moments are derived from moment-generating functions, while finite population moments are developed from corresponding infinite population moments using the finite probability operator defined in part 1 of this series.