Approximations to non-central distributions and their applications - Carter-Johnson, P C (Department of Mathematics and Applied Mathematics, 2023)
In testing hypotheses involving noncentral distributions percentage points are not always readily available and, if they are available, are not very well tabulated except, perhaps, for smaller degrees of freedom and noncentralities. Consequently,· for values that are not tabulated, interpolation, or, more likely, extrapolation of some kind is necessary, and the process can become tedious. In the case of calculations involving the power of the test, charts of the power of the F-test and t-test are available, but readings taken from these charts may be accurate to only one decimal place. In situations like the above, and in other cases, approximations are very useful and are sometimes as accurate, if not more so, than values obtained by interpolation (or extrapolation) or values read from charts. This thesis is chiefly concerned with applications in which approximations to the noncentral x2 , F, t and R distributions can be used. The approximations themselves, in most cases, are dealt with in a fair amount of detail to show the reader how they were obtained. Chapter 1 defines certain terms with which the reader may be unfamiliar, which are used in subsequent chapters. Chapters 2-5 deal with the approximations and their applications.· Each of these chapters is set out in the same way, section I am defining the noncentral distribution, section II dealing with the approximations, section III comparing the accuracy of the approximations with the exact values and section IV showing in which situations the approximations can be used.