NAG FL Interface
g01ecf (prob_​chisq)

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1 Purpose

g01ecf returns the lower or upper tail probability for the χ2-distribution with real degrees of freedom.

2 Specification

Fortran Interface
Function g01ecf ( tail, x, df, ifail)
Real (Kind=nag_wp) :: g01ecf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x, df
Character (1), Intent (In) :: tail
C Header Interface
#include <nag.h>
double  g01ecf_ (const char *tail, const double *x, const double *df, Integer *ifail, const Charlen length_tail)
The routine may be called by the names g01ecf or nagf_stat_prob_chisq.

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 Character(1) Input
On entry: indicates whether the upper or lower tail probability is required.
The lower tail probability is returned, i.e., P(Xx:ν).
The upper tail probability is returned, i.e., P(Xx:ν).
Constraint: tail='L' or 'U'.
2: x Real (Kind=nag_wp) Input
On entry: x, the value of the χ2 variate with ν degrees of freedom.
Constraint: x0.0.
3: df Real (Kind=nag_wp) Input
On entry: ν, the degrees of freedom of the χ2-distribution.
Constraint: df>0.0.
4: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value −1 is recommended since useful values can be provided in some output arguments even when ifail0 on exit. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
Note: in some cases g01ecf may return useful information.
If ifail=1, 2 or 3 on exit, then g01ecf returns 0.0.
On entry, tail=value.
Constraint: tail='L' or 'U'.
On entry, x=value.
Constraint: x0.0.
On entry, df=value.
Constraint: df>0.0.
The series used to calculate the gamma probabilities has failed to converge. The result returned should represent an approximation to the solution.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

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

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01ecf 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 s14baf.

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 (g01ecfe.f90)

10.2 Program Data

Program Data (g01ecfe.d)

10.3 Program Results

Program Results (g01ecfe.r)