nag_prob_gamma_vector (g01sfc) returns a number of lower or upper tail probabilities for the gamma distribution.
The lower tail probability for the gamma distribution with parameters
and
,
, 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
nag_incomplete_gamma (s14bac).
The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See
Section 2.6 in the g01 Chapter Introduction for further information.
- 1:
ltail – IntegerInput
On entry: the length of the array
tail.
Constraint:
.
- 2:
tail[ltail] – const Nag_TailProbabilityInput
On entry: indicates whether a lower or upper tail probability is required. For
, for
:
- The lower tail probability is returned, i.e., .
- The upper tail probability is returned, i.e., .
Constraint:
or , for .
- 3:
lg – IntegerInput
On entry: the length of the array
g.
Constraint:
.
- 4:
g[lg] – const doubleInput
On entry: , the value of the gamma variate with , .
Constraint:
, for .
- 5:
la – IntegerInput
On entry: the length of the array
a.
Constraint:
.
- 6:
a[la] – const doubleInput
On entry: the parameter of the gamma distribution with , .
Constraint:
, for .
- 7:
lb – IntegerInput
On entry: the length of the array
b.
Constraint:
.
- 8:
b[lb] – const doubleInput
On entry: the parameter of the gamma distribution with , .
Constraint:
, for .
- 9:
p[] – doubleOutput
-
Note: the dimension,
dim, of the array
p
must be at least
.
On exit: , the probabilities of the beta distribution.
- 10:
ivalid[] – IntegerOutput
-
Note: the dimension,
dim, of the array
ivalid
must be at least
.
On exit:
indicates any errors with the input arguments, with
- No error.
-
On entry, | invalid value supplied in tail when calculating . |
-
-
On entry, | , |
or | . |
- The solution did not converge in iterations, see nag_incomplete_gamma (s14bac) for details. The probability returned should be a reasonable approximation to the solution.
- 11:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
Not applicable.
The time taken by nag_prob_gamma_vector (g01sfc) to calculate each probability varies slightly with the input arguments , and .
This example reads in values from a number of gamma distributions and computes the associated lower tail probabilities.