nag_deviates_normal (g01fac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_deviates_normal (g01fac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_deviates_normal (g01fac) returns the deviate associated with the given probability of the standard Normal distribution.

2  Specification

#include <nag.h>
#include <nagg01.h>
double  nag_deviates_normal (Nag_TailProbability tail, double p, NagError *fail)

3  Description

The deviate, xp associated with the lower tail probability, p, for the standard Normal distribution is defined as the solution to
ZX=12πe-X2/2,   -<X< .
The method used is an extension of that of Wichura (1988). p is first replaced by q=p-0.5.
(a) If q0.3, xp is computed by a rational Chebyshev approximation
xp=sAs2 Bs2 ,
where s=2πq and A, B are polynomials of degree 7.
(b) If 0.3<q0.42, xp is computed by a rational Chebyshev approximation
xp=signq Ct Dt ,
where t=q-0.3 and C, D are polynomials of degree 5.
(c) If q>0.42, xp is computed as
xp=signq Eu Fu +u ,
where u = -2 × log minp,1-p  and E, F are polynomials of degree 6.
For the upper tail probability -xp is returned, while for the two tail probabilities the value xp* is returned, where p* is the required tail probability computed from the input value of p.

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
Wichura (1988) Algorithm AS 241: the percentage points of the Normal distribution Appl. Statist. 37 477–484

5  Arguments

1:     tailNag_TailProbabilityInput
On entry: indicates which tail the supplied probability represents.
The lower probability, i.e., PXxp.
The upper probability, i.e., PXxp.
The two tail (significance level) probability, i.e., PXxp+PX-xp.
The two tail (confidence interval) probability, i.e., PXxp-PX-xp.
Constraint: tail=Nag_LowerTail, Nag_UpperTail, Nag_TwoTailSignif or Nag_TwoTailConfid.
2:     pdoubleInput
On entry: p, the probability from the standard Normal distribution as defined by tail.
Constraint: 0.0<p<1.0.
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

If on exit fail.code= NE_NOERROR, then nag_deviates_normal (g01fac) returns 0.0.
On entry, argument value had an illegal value.
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.
On entry, p=value.
Constraint: p<1.0.
On entry, p=value.
Constraint: p>0.0.

7  Accuracy

The accuracy is mainly limited by the machine precision.

8  Parallelism and Performance

Not applicable.

9  Further Comments


10  Example

Four values of tail and p are input and the deviates calculated and printed.

10.1  Program Text

Program Text (g01face.c)

10.2  Program Data

Program Data (g01face.d)

10.3  Program Results

Program Results (g01face.r)

nag_deviates_normal (g01fac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014