Chi-Square Distribution Critical Value Formulas

Below you will find descriptions and details for the 3 formulas that are used to compute critical values of the chi-square distribution.

Cumulative distribution function (CDF) for the chi-square distribution:

Variable definitions:
γ(s, x) = lower incomplete gamma function
Γ(z) = gamma function

Gamma function:

Lower incomplete gamma function:

Variable definitions:
x = upper limit of integration
s = value of the shape parameter