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How are the values in chi-square distribution tables derived for different values of $\alpha$ and degrees of freedom, given the PDF? Any help appreciated.

Vishal Sharma
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  • How could the c.d.f. not be useful for this? Those tables are tables of values of the c.d.f. or its inverse. – Michael Hardy Feb 26 '18 at 16:52
  • Sorry, meant to ask how the values are derived, given the PDF – Vishal Sharma Feb 26 '18 at 17:02
  • For some values of the 'degrees of freedom' parameter (DF), the CDF can be expr in closed form, and tabled values can be computed by calculus. An exmp is when DF = 2, so that CHISQ(2) is an exponential distribution. Otherwise, numerical integration is the straightforward method. // There are some rational function approximations of the CDF (e.g., truncated series expansions) that are good enough over certain ranges of DFs to give several places of accuracy. // Nowadays, stat software gives v. good values. Exmp: in R qchisq(.95, 5) returns 11.0705, where qchisq is quantile fcn, inv CDF. – BruceET Feb 26 '18 at 18:22
  • Maybe see Wikipedia for some details. – BruceET Feb 26 '18 at 18:28
  • Maybe also, for more on numerical integration:. – BruceET Feb 26 '18 at 18:44

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