NAG CL Interface
g01gec (prob_​beta_​noncentral)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{x}$ – double Input

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

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

2: $\mathbf{a}$ – double Input

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

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

3: $\mathbf{b}$ – double Input

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

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

4: $\mathbf{lambda}$ – double Input

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 X02AMC.

5: $\mathbf{tol}$ – double Input

On entry: the relative accuracy required by you in the results. If g01gec is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see X02AJC), the value of $10\times \mathit{machine precision}$ is used instead.

See Section 7 for the relationship between tol and max_iter.

6: $\mathbf{max\_iter}$ – Integer Input

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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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. 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 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

10.2 Program Data

10.3 Program Results