| This dissertation is concerned with the evaluation of some of the special functions of probability and statistics, with emphasis on the normal probability distribution, the gamma function and the incomplete gamma function.;A number of continued fractions are developed: for computing the gamma function, the logarithm of the gamma function, and the incomplete gamma function. Two short, accurate methods for evaluating the incomplete gamma function are developed. They lead to Fortran programs of 30 and 40 lines, listed in the dissertation, that compare favorably with much larger Fortran programs based on published methods or in scientific subroutine packages such as IMSL.;Two new methods for evaluating the normal probability distribution are developed; one is a very fast method that gives full possible accuracy in single precision, the other gives relative accuracy of 10;A method for transforming ;Portions of this dissertation have been published, or have been accepted for publication: the extension of Ramanujan's rational approximation to... |
