nag_prob_normal (g01eac) (PDF version)
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g01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_prob_normal (g01eac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_prob_normal (g01eac) returns a one or two tail probability for the standard Normal distribution.

2  Specification

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

3  Description

The lower tail probability for the standard Normal distribution, PXx is defined by:
PXx=-xZXdX,
where
ZX=12π e-X2/2, -<X< .
The relationship
PXx=12erfc-x2
is used, where erfc is the complementary error function, and is computed using nag_erfc (s15adc). For the upper tail probability the relationship PXx=PX-x is used and for the two tail significance level probability twice the probability obtained from the absolute value of x is returned.
When the two tail confidence probability is required the relationship
PXx-PX-x=erfx2 ,
is used, where erf is the error function, and is computed using nag_erf (s15aec).

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

5  Arguments

1:     tailNag_TailProbabilityInput
On entry: indicates which tail the returned probability should represent.
tail=Nag_LowerTail
The lower tail probability is returned, i.e., PXx.
tail=Nag_UpperTail
The upper tail probability is returned, i.e., PXx.
tail=Nag_TwoTailSignif
The two tail (significance level) probability is returned, i.e., PXx+PX-x.
tail=Nag_TwoTailConfid
The two tail (confidence interval) probability is returned, i.e., PXx-PX-x.
Constraint: tail=Nag_LowerTail, Nag_UpperTail, Nag_TwoTailSignif or Nag_TwoTailConfid.
2:     xdoubleInput
On entry: x, the value of the standard Normal variate.
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
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.

7  Accuracy

Accuracy is limited by machine precision. For detailed error analysis see nag_erfc (s15adc) and nag_erf (s15aec).

8  Further Comments

None.

9  Example

Four values of tail and x are input and the probabilities calculated and printed.

9.1  Program Text

Program Text (g01eace.c)

9.2  Program Data

Program Data (g01eace.d)

9.3  Program Results

Program Results (g01eace.r)


nag_prob_normal (g01eac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012