NAG Library Function Document

nag_prob_non_central_beta_dist (g01gec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}$ – doubleInput

On entry: $\beta$, the deviate from the beta distribution, for which the probability $P\left(B\le \beta :a,b\text{;}\lambda \right)$ is to be found.

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

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:    $\mathbf{lambda}$ – doubleInput

On entry: $\lambda$, the noncentrality parameter of the required beta distribution.

Constraint: $0.0\le \mathbf{lambda}\le -2.0\log \left(U\right)$, where $U$ is the safe range parameter as defined by nag_real_safe_small_number (X02AMC).

5:    $\mathbf{tol}$ – doubleInput

On entry: the relative accuracy required by you in the results. If nag_prob_non_central_beta_dist (g01gec) 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.

See Section 7 for the relationship between tol and max_iter.

6:    $\mathbf{max\_iter}$ – IntegerInput

On entry: the maximum number of iterations that the algorithm should use.

See Section 7 for suggestions as to suitable values for max_iter for different values of the arguments.

Suggested value: $500$.

Constraint: $\mathbf{max\_iter}\ge 1$.

7:    $\mathbf{fail}$ – 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

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_CONV

The solution has failed to converge in $〈\mathit{\text{value}}〉$ iterations. Consider increasing max_iter or tol. The returned value will be an approximation to the correct value.

NE_INT_ARG_LT

On entry, $\mathbf{max\_iter}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{max\_iter}\ge 1$.

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_PROB_B_INIT

The required accuracy was not achieved when calculating the initial value of the beta distribution. You should try a larger value of tol. The returned value will be an approximation to the correct value. This error exit is no longer possible but is still documented for historical reasons.

NE_PROB_LIMIT

The probability is too close to 0.0 or 1.0 for the algorithm to be able to calculate the required probability. nag_prob_non_central_beta_dist (g01gec) will return 0.0 or 1.0 as appropriate. This should be a reasonable approximation.

NE_REAL_ARG_CONS

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{a}\le {10}^6$.

On entry, $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{b}\le {10}^6$.

On entry, $\mathbf{lambda}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{lambda}\le -2.0\log \left(U\right)$, where $U$ is the safe range parameter as defined by nag_real_safe_small_number (X02AMC).

On entry, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{x}\le 1.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01gece.c)

10.2

Program Data

Program Data (g01gece.d)

10.3

Program Results

Program Results (g01gece.r)