Computer implementation of probability distribution quantile estimation

Generally, we get probability distribution quantile by looking through numerical tables, however, it is not only easy to make mistake, but also limited in precision, no more than 0.0001. And programming techniques up to now are either too restrictive to be applied to general cases, or too complicated to be implemented for practical use. Therefore, there is a need for robust procedures to estimate quantiles, which can be applied to relatively generic processes and easy to implement. The paper briefly discusses the algorithm and the implement of some familiar probability distribution quantiles, such as, standardized normal distribution, β distribution, X² distribution, t distribution and F distribution. Especially, we use Newton dichotomy here to improve the precision, in the case of t and F distributions which is insufficient by approximate formulae only, because of the accumulated error. An experimental performance evaluation demonstrates the validity of these procedures to calculate probability distribution quantiles.