Simple approximations of some statistical functions

TL;DR

This paper proposes simple, accurate approximation formulas for key statistical distribution quantiles to facilitate hypothesis testing computations in practical scenarios.

Contribution

It introduces new approximation expressions for the inverse normal, Student's t, and outlier rejection criteria distributions, simplifying their computation.

Findings

Approximate formulas are accurate for most practical applications.

Simplifications reduce computational complexity in statistical hypothesis testing.

The methods are applicable to common statistical distributions used in practice.

Abstract

Possibilities are considered to simplify the computation of several statistical functions used to test statistical hypotheses when processing observations: the inverse normal distribution, the Student's t-distribution, and the criterion for rejecting outliers. For these three cases, simple approximation expressions are proposed for the quantiles of these statistical distributions, which are accurate enough for most practical applications.