nag_prob_beta_dist (g01eec) computes the upper and lower tail probabilities and the probability density function of the beta distribution with parameters and .
The probability density function of the beta distribution with parameters
and
is:
The lower tail probability,
is defined by
The function
, also known as the incomplete beta function is calculated using
nag_incomplete_beta (s14ccc).
- 1:
x – doubleInput
On entry: , the value of the beta variate.
Constraint:
.
- 2:
a – doubleInput
On entry: , the first parameter of the required beta distribution.
Constraint:
.
- 3:
b – doubleInput
On entry: , the second parameter of the required beta distribution.
Constraint:
.
- 4:
tol – doubleInput
On entry: this argument is no longer referenced, but is included for backwards compatability.
- 5:
p – double *Output
On exit: the lower tail probability, .
- 6:
q – double *Output
On exit: the upper tail probability, .
- 7:
pdf – double *Output
On exit: the probability density function, .
- 8:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
The accuracy is limited by the error in the incomplete beta function. See
Section 7 in nag_incomplete_beta (s14ccc) for further details.
Not applicable.
None.
This example reads values from a number of beta distributions and computes the associated upper and lower tail probabilities and the corresponding value of the probability density function.