Continued Fractions Evaluation And Their Applications To Some Probability Distribution Functions

Abstract

This paper discusses some continued fractions in obtaining rational approximations to functions, emphasising those which are important in statistical applications. It will be shown that continued fractions are valuable tools in the evaluation of certain cumulative distribution functions. The probabilities of several convergents were evaluated over a wide range of functions, to determine the effectiveness of the expansion. Also forward and backward methods were used. However in conclusion, the continued fraction method as a mean of obtaining rational approximations to probability distributions is a very powerful and effective technique.