sigLevel.c File Reference

Detailed Description

Routines for Student's t distribution, the F distribution, the linear-correlation coefficient distribution, and Poisson distribution.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

M. Borland, C. Saunders, R. Soliday

Definition in file sigLevel.c.

#include "mdb.h"

Go to the source code of this file.

Functions
double	normSigLevel (double z0, long tails)
	Computes the probability that a standard normal variable exceeds a given value.
double	ChiSqrSigLevel (double ChiSquared0, long nu)
	Computes the probability that a chi-squared variable exceeds a given value.
double	tTailSigLevel (double t0, long nu, long tails)
	Computes the probability that the absolute value of a t-distributed variable exceeds a given value.
double	FSigLevel (double var1, double var2, long nu1, long nu2)
	Computes the probability that an F-distributed variable exceeds a given value.
double	rSigLevel (double r0, long nu)
	Computes the probability that the linear correlation coefficient exceeds a given value.
double	poissonSigLevel (long n, double n0)
	Computes the probability that a Poisson-distributed random variable exceeds or equals a given value.

Function Documentation

ChiSqrSigLevel()

double ChiSqrSigLevel	(	double	ChiSquared0,
		long	nu )

Computes the probability that a chi-squared variable exceeds a given value.

This function calculates the probability that a chi-squared random variable with nu degrees of freedom exceeds ChiSquared0.

Parameters

ChiSquared0	The chi-squared value for which the probability is computed.
nu	The degrees of freedom of the chi-squared distribution.

Returns

The probability that the chi-squared variable exceeds ChiSquared0 for nu degrees of freedom. Returns -1 if ChiSquared0 is negative.

Definition at line 64 of file sigLevel.c.

{
  if (ChiSquared0 < 0)
    return -1;
  return gammaQ(nu / 2.0, ChiSquared0 / 2);
}

FSigLevel()

double FSigLevel	(	double	var1,
		double	var2,
		long	nu1,
		long	nu2 )

Computes the probability that an F-distributed variable exceeds a given value.

This function calculates the probability that an F-distributed random variable with nu1 and nu2 degrees of freedom exceeds F0, where F0 is defined as Max(var1, var2) / Min(var1, var2).

Parameters

var1	The first variance.
var2	The second variance.
nu1	The degrees of freedom associated with var1.
nu2	The degrees of freedom associated with var2.

Returns

The probability that F exceeds F0 for nu1 and nu2 degrees of freedom.

Definition at line 101 of file sigLevel.c.

{
  if (var1 < var2) {
    SWAP_DOUBLE(var1, var2);
    SWAP_LONG(nu1, nu2);
  }
  return betaInc(nu2 / 2.0, nu1 / 2.0, nu2 / (nu2 + nu1 * var1 / var2));
}

normSigLevel()

double normSigLevel	(	double	z0,
		long	tails )

Computes the probability that a standard normal variable exceeds a given value.

This function calculates the probability that a standard normal random variable Z satisfies Z > z0.

Parameters

z0	The value for which the probability is computed.
tails	Specifies whether to compute a one-tailed (1) or two-tailed (2) probability.

Returns

The probability that Z exceeds z0. Returns -1 if the number of tails is invalid.

Definition at line 40 of file sigLevel.c.

{
  if (z0 < 0)
    z0 = -z0;
  if (tails != 1 && tails != 2)
    return -1;
#if defined(vxWorks)
  fprintf(stderr, "erfc function is not implemented on vxWorks\n");
  exit(1);
#else
  return erfc(z0 / SQRT2) / (tails == 1 ? 2 : 1);
#endif
}

poissonSigLevel()

double poissonSigLevel	(	long	n,
		double	n0 )

Computes the probability that a Poisson-distributed random variable exceeds or equals a given value.

This function calculates the probability that the number of events n is greater than or equal to a specified value n0, given a Poisson distribution with an expected number of events n0.

Parameters

n	The number of events observed.
n0	The expected number of events.

Returns

The probability that n or more events are observed given a Poisson distribution with n0 expected events.

Definition at line 141 of file sigLevel.c.

{
  double sum, term, result = 0;
  long i;
  if (n == 0)
    return 1;
  if (n < 0 || n0 <= 0) {
    return n0 < n ? 0 : 1;
  }
  if (n0 > 200) {
    result = normSigLevel((n - n0) / sqrt(n0), 1);
    if (n < n0)
      return 1 - result;
    return result;
  }
  if (!exp(-n0))
    return n0 < n ? 0 : 1;
  sum = 1;
  term = 1;
  i = 0;
  while (++i < n) {
    term *= n0 / i;
    sum += term;
  }
  result = 1 - sum * exp(-n0);
  if (isnan(result)) {
    return n0 < n ? 0 : 1;
  }
  if (result < 0)
    return 0;
  return result;
}

rSigLevel()

double rSigLevel	(	double	r0,
		long	nu )

Computes the probability that the linear correlation coefficient exceeds a given value.

This function calculates the probability that the linear correlation coefficient r exceeds |r0| for nu degrees of freedom.

Parameters

r0	The correlation coefficient value.
nu	The degrees of freedom.

Returns

The probability that the linear correlation coefficient exceeds |r0| for nu degrees of freedom. Returns -1 if nu is less than 2 or if r0 is not in the valid range.

Definition at line 120 of file sigLevel.c.

{
  if (r0 < 0)
    r0 = -r0;
  if (nu < 2)
    return -1;
  if (r0 >= 1)
    return 0;
  return tTailSigLevel(r0 * sqrt(nu / (1 - r0 * r0)), nu, 2);
}

tTailSigLevel()

double tTailSigLevel	(	double	t0,
		long	nu,
		long	tails )

Computes the probability that the absolute value of a t-distributed variable exceeds a given value.

This function calculates the probability that |t| > t0 for a t-distribution with nu degrees of freedom.

Parameters

t0	The t-value for which the probability is computed.
nu	The degrees of freedom of the t-distribution.
tails	Specifies whether to compute a one-tailed (1) or two-tailed (2) probability.

Returns

The probability that |t| exceeds t0 for nu degrees of freedom. Returns -1 if the number of tails is invalid.

Definition at line 82 of file sigLevel.c.

{
  if (tails != 1 && tails != 2)
    return -1;
  return betaInc(nu / 2.0, 0.5, nu / (nu + t0 * t0)) / (tails == 1 ? 2 : 1);
}