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IMSL_FCDF

# IMSL_FCDF

The IMSL_FCDF function evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.

The IMSL_FCDF function evaluates the distribution function of a Snedecorâs F random variable with dfnum and dfden. The function is evaluated by making a transformation to a beta random variable and then evaluating the incomplete beta function. If X is an F variate with Î½1 and Î½2 degrees of freedom and Y = (Î½1X)/(Î½2 + Î½1X), then Y is a beta variate with parameters p = Î½1/2 and q = Î½2/2. The IMSL_FCDF function also uses a relationship between F random variables that is expressed as follows: FF(f, Î½1, Î½2) = 1 â FF(1/f, Î½2, Î½1), where FF is the distribution function for an F random variable.

If INVERSE is specified, the IMSL_FCDF function evaluates the inverse distribution function of a Snedecorâs F random variable with Î½1 = dfnum numerator degrees of freedom and Î½2 = dfden denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then evaluating the inverse of an incomplete beta function.

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