NAG Library Function Document

nag_deviates_beta (g01fec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{p}$ – doubleInput

On entry: $p$, the lower tail probability from the required beta distribution.

Constraint: $0.0\le \mathbf{p}\le 1.0$.

2:    $\mathbf{a}$ – doubleInput

On entry: $a$, the first parameter of the required beta distribution.

Constraint: $0.0<\mathbf{a}\le {10}^6$.

3:    $\mathbf{b}$ – doubleInput

On entry: $b$, the second parameter of the required beta distribution.

Constraint: $0.0<\mathbf{b}\le {10}^6$.

4:    $\mathbf{tol}$ – doubleInput

On entry: the relative accuracy required by you in the result. If nag_deviates_beta (g01fec) is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see nag_machine_precision (X02AJC)), the value of $10\times \mathit{machine precision}$ is used instead.

5:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

On any of the error conditions listed below except $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_RES_NOT_ACC or NE_SOL_NOT_CONV nag_deviates_beta (g01fec) returns $0.0$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL_ARG_GT

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}\le {10}^6$.

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{b}\le {10}^6$.

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}\le 1.0$.

NE_REAL_ARG_LE

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}>0.0$.

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{b}>0.0$.

NE_REAL_ARG_LT

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}\ge 0.0$.

NE_RES_NOT_ACC

The requested accuracy has not been achieved. Use a larger value of tol. There is doubt concerning the accuracy of the computed result. $100$ iterations of the Newton–Raphson method have been performed without satisfying the accuracy criterion (see Section 9). The result should be a reasonable approximation of the solution.

NE_SOL_NOT_CONV

The solution has failed to converge. However, the result should be a reasonable approximation. Requested accuracy not achieved when calculating beta probability. You should try setting tol larger.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01fece.c)

10.2

Program Data

Program Data (g01fece.d)

10.3

Program Results

Program Results (g01fece.r)