Critical Values of Some Probability Distributions and Standard Numerical Methods

Abstract

Statistic processing of experimental data, part of which is use of interval estimation, statistic hypothesis tests, and other statistical methods, requires critical values of some probability distributions. To obtain critical values, critical values tables are usually used, which are part of literature focused on mentioned statistical methods. Significant disadvantage of mentioned approach is the limited number of discrete values. If it is required to process large amount of experimental data using own programs, then it is appropriate to possess suitable critical values calculation methods. Presented article is focused on critical values calculation methods for standardized normal distribution, Student’s t-distribution, Fisher-Snedecor F-distribution, and χ^2-distribution using standard numerical methods, specifically approximate calculation of definite integrals and approximate solving of nonlinear equations.