A summary of confidence interval estimation of standard and certain non-centrality parameters

Abstract

In this thesis, confidence bounds on simple and more complex parameters are stated along with detailed computational procedures for finding these confidence bounds from the given data.

Confidence bounds on the more familiar parameters, i.e., μ, ơ², μ₁ - μ₂, and ơ²₁/ơ²₂, are briefly presented for the sake of completeness. The confidence statements for the less familiar parameters and combinations of parameters are treated in more detail.

In the cases of the non-centrality parameters of the non-central t², F and X² distributions, a variance-stabilizing transformation is used, a normal approximation is utilized, and confidence bounds are pub on the parameter. In the non-central t² and non-central F distributions iterative procedures are used to obtain confidence bounds on the non-centrality parameter, i.e., a first guess is made which is improved until the desired accuracy is obtained

This procedure is unnecessary in the non-central X² distribution, since the expressions for the upper and lower limits can be reduced to closed form.

Computational procedures and completely worked examples are included.