NAG CL Interface
g01ecc (prob_​chisq)

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1 Purpose

g01ecc returns the lower or upper tail probability for the χ2-distribution with real degrees of freedom.

2 Specification

#include <nag.h>
double  g01ecc (Nag_TailProbability tail, double x, double df, NagError *fail)
The function may be called by the names: g01ecc, nag_stat_prob_chisq or nag_prob_chi_sq.

3 Description

The lower tail probability for the χ2-distribution with ν degrees of freedom, P(Xx:ν) is defined by:
P(Xx:ν)=12ν/2Γ(ν/2) 0.0xXν/2-1e-X/2dX,  x0,ν>0.  
To calculate P(Xx:ν) a transformation of a gamma distribution is employed, i.e., a χ2-distribution with ν degrees of freedom is equal to a gamma distribution with scale parameter 2 and shape parameter ν/2.

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 whether the upper or lower tail probability is required.
tail=Nag_LowerTail
The lower tail probability is returned, i.e., P(Xx:ν).
tail=Nag_UpperTail
The upper tail probability is returned, i.e., P(Xx:ν).
Constraint: tail=Nag_LowerTail or Nag_UpperTail.
2: x double Input
On entry: x, the value of the χ2 variate with ν degrees of freedom.
Constraint: x0.0.
3: df double Input
On entry: ν, the degrees of freedom of the χ2-distribution.
Constraint: df>0.0.
4: 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_CHARACTER, NE_REAL_ARG_LE or NE_REAL_ARG_LT on exit, then g01ecc returns 0.0.
NE_ALG_NOT_CONV
The series used to calculate the gamma probabilities has failed to converge. The result returned should represent an approximation to the solution.
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.
NE_REAL_ARG_LE
On entry, df=value.
Constraint: df>0.0.
NE_REAL_ARG_LT
On entry, x=value.
Constraint: x0.0.

7 Accuracy

A relative accuracy of five significant figures is obtained in most cases.

8 Parallelism and Performance

g01ecc is not threaded in any implementation.

9 Further Comments

For higher accuracy the transformation described in Section 3 may be used with a direct call to s14bac.

10 Example

Values from various χ2-distributions are read, the lower tail probabilities calculated, and all these values printed out, until the end of data is reached.

10.1 Program Text

Program Text (g01ecce.c)

10.2 Program Data

Program Data (g01ecce.d)

10.3 Program Results

Program Results (g01ecce.r)