for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $b_{0} < 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0});$

for

2 < a_{0} < 8

a_{0}

is reduced to the interval

[1, 2]

B (a, b) = \frac{a_{0} - 1}{a_{0} + b_{0} - 1} B (a_{0} - 1, b_{0})

;

for

1 \leq a_{0} \leq 2

for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $2 < b_{0} < 8$ , $b_{0}$ is reduced to the interval $[1, 2]$ ;
for $b_{0} \leq 2$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0}) .$

s14cbf is derived from BETALN in DiDonato and Morris (1992).

4 References

DiDonato A R and Morris A H (1992) Algorithm 708: Significant digit computation of the incomplete beta function ratios ACM Trans. Math. Software 18 360–373

5 Arguments

1: $a$ – Real (Kind=nag_wp) Input: On entry: the argument $a$ of the function.

Constraint: $a > 0.0$ .
2: $b$ – Real (Kind=nag_wp) Input: On entry: the argument $b$ of the function.

Constraint: $b > 0.0$ .
3: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $a = ⟨ value ⟩$ .
Constraint: $a > 0.0$ .

On entry, $b = ⟨ value ⟩$ .
Constraint: $b > 0.0$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

s14cbf should produce full relative accuracy for all input arguments.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

s14cbf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of the arguments

a

and

b

from a file, evaluates the function and prints the results.

s14cb: FL CL CPP AD PY MB

NAG FL Interfaces14cbf (beta_​log_​real)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
s14cbf (beta_log_real)