-
distribution arises as the ratio of two chi-squared distributions:
University Maths Notes: Probability and Statistics – The F - Distribution
The-
distribution arises as the ratio of two chi-squared distributions:
where
and
have
chi-square distributions with
and
degrees
of freedom respectively, and
andare
independent.
The mean, variance and skew are
and
respectively.
The probability density function of an
distributed
random variable is given by
for
real
whereand
are
positive integers, and
is
the beta function.
The cumulative distribution function is
where
is
the regularized incomplete beta function.