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NAG CL Interface
g01eac (prob_​normal)

NAG Library Manual, Mark 28.7
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG CL Interface Introduction
G01 (Stat) Chapter Contents
G01 (Stat) Chapter Introduction
g01ea:  FL   CL   CPP   AD   PY   MB 

▸▿ Contents

© The Numerical Algorithms Group Ltd. 2022
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1 Purpose

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

2 Specification

#include <nag.h>
double  g01eac (Nag_TailProbability tail, double x, NagError *fail)
The function may be called by the names: g01eac, nag_stat_prob_normal or nag_prob_normal.

3 Description

The lower tail probability for the standard Normal distribution, P(X≤x) is defined by:
P(X≤x)=∫-∞xZ(X)dX,  
where
Z(X)=12π e-X2/2, -∞<X< ∞.  
The relationship
P(X≤x)=12erfc(-x2)  
is used, where erfc is the complementary error function, and is computed using s15adc. For the upper tail probability the relationship P(X≥x)=P(X≤-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
P(X≤|x|)-P(X≤-|x|)=erf(|x|2) ,  
is used, where erf is the error function, and is computed using s15aec.

4 References

NIST Digital Library of Mathematical Functions
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

5 Arguments

1: tail – Nag_TailProbability Input
On entry: indicates which tail the returned probability should represent.
tail=Nag_LowerTail
The lower tail probability is returned, i.e., P(X≤x).
tail=Nag_UpperTail
The upper tail probability is returned, i.e., P(X≥x).
tail=Nag_TwoTailSignif
The two tail (significance level) probability is returned, i.e., P(X≥|x|)+P(X≤-|x|).
tail=Nag_TwoTailConfid
The two tail (confidence interval) probability is returned, i.e., P(X≤|x|)-P(X≤-|x|).
Constraint: tail=Nag_LowerTail, Nag_UpperTail, Nag_TwoTailSignif or Nag_TwoTailConfid.
2: x – double Input
On entry: x, the value of the standard Normal variate.
3: 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

If fail.code= NE_NOERROR, then g01eac returns 0.0.
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_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.
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.

7 Accuracy

Accuracy is limited by machine precision. For detailed error analysis see s15adc and s15aec.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01eac is not threaded in any implementation.

9 Further Comments

None.

10 Example

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

10.1 Program Text

Program Text (g01eace.c)

10.2 Program Data

Program Data (g01eace.d)

10.3 Program Results

Program Results (g01eace.r)
NAG Library Manual, Mark 28.7
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG CL Interface Introduction
G01 (Stat) Chapter Contents
G01 (Stat) Chapter Introduction
g01ea:  FL   CL   CPP   AD   PY   MB 
© The Numerical Algorithms Group Ltd. 2022