Cdf.Gamma Method |
Namespace: Imsl.Stat
Method Cdf.Gamma evaluates the distribution function, F, of a gamma random variable with shape parameter a; that is,
where is the gamma
function. (The gamma function is the integral from 0 to
of the same integrand as above). The value of the
distribution function at the point x is the
probability that the random variable takes a value less than or
equal to x.
The gamma distribution is often defined as a two-parameter
distribution with a scale parameter b (which must be
positive), or even as a three-parameter distribution in which the
third parameter c is a location parameter. In the most
general case, the probability density function over is
If T is such a random variable with parameters
a, b, and c, the probability that can be obtained from Cdf.Gamma by setting
.
If X is less than a or if X is less than or equal to 1.0, Cdf.Gamma uses a series expansion. Otherwise, a continued fraction expansion is used. (See Abramowitz and Stegun, 1964.)