Gamma cumulative distribution function
gamcdf(x,a,b)
[p,plo,pup] = gamcdf(x,a,b,pcov,alpha)
[p,plo,pup] = gamcdf(___,'upper')
gamcdf(x,a,b)
returns the gamma cdf at each of the
values in x
using the corresponding shape parameters in
a
and scale parameters in b
.
x
, a
, and b
can be vectors,
matrices, or multidimensional arrays that all have the same size. A scalar input is
expanded to a constant array with the same dimensions as the other inputs. The
parameters in a
and b
must be positive, and the
values in x
must lie on the interval
[0 Inf]
.
[p,plo,pup] = gamcdf(x,a,b,pcov,alpha)
produces
confidence bounds for p
when the input parameters a
and b
are
estimates. pcov
is a 2-by-2 matrix containing the
covariance matrix of the estimated parameters. alpha
has
a default value of 0.05, and specifies 100(1-alpha)
%
confidence bounds. plo
and pup
are
arrays of the same size as p
containing the lower
and upper confidence bounds.
[p,plo,pup] = gamcdf(___,'upper')
returns
the complement of the gamma cdf at each value in x
,
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use the 'upper'
argument
with any of the previous syntaxes.
The gamma cdf is
The result, p, is the probability that a single observation from a gamma distribution with parameters a and b will fall in the interval [0 x].
gammainc
is the gamma distribution with b fixed
at 1.