The lower tail probability for the gamma distribution with parameters
, is defined by:
The mean of the distribution is
and its variance is
. The transformation
is applied to yield the following incomplete gamma function in normalized form,
This is then evaluated using s14bac
The result should have a relative accuracy of machine precision
. There are rare occasions when the relative accuracy attained is somewhat less than machine precision
but the error should not exceed more than
decimal places. Note also that there is a limit of
decimal places on the achievable accuracy, because constants in s14bac
are given to this precision.
The time taken by g01efc
varies slightly with the input arguments g
This example reads in values from a number of gamma distributions and computes the associated lower tail probabilities.