The relationships between discrete and continuous probability distributions

TR Number
Journal Title
Journal ISSN
Volume Title
Virginia Polytechnic Institute

Though some of the discrete distributions, for example the binomial, hypergeometric, Poisson, are well tabulated, often statisticians use the percentage points of approximating continuous distributions when analysing discrete data. In this thesis, the exact relationships between certain discrete and continuous distributions are established, and these relationships are used for setting confidence limits and significance testing of hypotheses.

In Chapter 1, statements of all distributions and mathematical functions used in this thesis are made, and also some approximations are mentioned without proofs.

In Chapter 2, exact relationships between discrete distributions (the binomial, negative-binomial, and Poisson) and continuous distributions (the F and χ²) are proved.

In Chapter 3, use is made of the approximate and exact relationships between discrete and continuous distributions, for setting confidence limits on the parameters of the discrete distributions.

Chapter 4 consists of the approximate and exact significance testing of hypotheses by using the approximate and exact relationships, given in Chapter 2.

In Chapter 5, two-sample, exact and approximate, significance tests of hypotheses on the Poisson distribution are performed, in the case of fixed number of events experimentation and fixed time experimentation.