/* Function: esl_sxp_logcdf()
*
* Purpose: Calculates the log of the cumulative distribution function for the
* stretched exponential pdf, $\log P(X \leq x)$, given
* quantile <x>, offset <mu>, and parameters <lambda> and <tau>.
*/
double
esl_sxp_logcdf(double x, double mu, double lambda, double tau)
{
double y = lambda * (x-mu);
double val;
if (x <= mu) return -eslINFINITY;
esl_stats_IncompleteGamma(1./tau, exp(tau * log(y)), &val, NULL);
return log(val);
}
/* Function: esl_gam_cdf()
* Incept: SRE, Mon Nov 14 12:47:36 2005 [HHMI HQ]
*
* Purpose: Calculates the cumulative distribution function
* for the gamma, $P(X \leq x)$, given value <x>,
* location parameter <mu>, scale parameter <lambda>, and
* shape parameter <tau>.
*
* (For $\mu=0$, $\lambda = 1$, this is the
* incomplete Gamma function $P(\tau,x)$.)
*/
double
esl_gam_cdf(double x, double mu, double lambda, double tau)
{
double y = lambda * (x - mu);
double val;
if (y <= 0.) return 0.;
esl_stats_IncompleteGamma(tau, y, &val, NULL);
return val;
}
/* Function: esl_gam_logsurv()
* Incept: SRE, Mon Nov 14 13:14:05 2005 [HHMI HQ]
*
* Purpose: Calculates the log of the survival function for the gamma,
* $\log P(X > x)$, given value <x>, location parameter <mu>,
* scale parameter <lambda>, and shape parameter <tau>.
*
* Relies on <esl_stats_IncompleteGamma()>, which has limited
* dynamic range. Any result of < -700 or so will be -infinity.
* To fix this, we need a log version of <esl_stats_IncompleteGamma()>.
*/
double
esl_gam_logsurv(double x, double mu, double lambda, double tau)
{
double y = lambda * (x - mu);
double val;
if (y <= 0.) return 0.;
esl_stats_IncompleteGamma(tau, y, NULL, &val);
return log(val);
}
/* Function: esl_gam_logcdf()
* Incept: SRE, Mon Nov 14 13:10:21 2005 [HHMI HQ]
*
* Purpose: Calculates the log of the cumulative distribution function
* for the gamma, $\log P(X \leq x)$, given value <x>, location
* parameter <mu>, scale parameter <lambda>, and shape
* parameter <tau>.
*/
double
esl_gam_logcdf(double x, double mu, double lambda, double tau)
{
double y = lambda * (x - mu);
double val;
if (y <= 0.) return -eslINFINITY;
esl_stats_IncompleteGamma(tau, y, &val, NULL);
return log(val);
}
/* Function: esl_sxp_logsurv()
*
* Purpose: Calculates the log survival function for the
* stretched exponential pdf, $\log P(X > x)$, given
* quantile <x>, offset <mu>, and parameters <lambda> and <tau>.
*/
double
esl_sxp_logsurv(double x, double mu, double lambda, double tau)
{
double y = lambda * (x-mu);
double val;
if (x <= mu) return 0.0;
esl_stats_IncompleteGamma(1./tau, exp(tau * log(y)), NULL, &val);
return log(val);
}
/* Function: esl_sxp_cdf()
*
* Purpose: Calculates the cumulative distribution function for the
* stretched exponential pdf, $P(X \leq x)$, given
* quantile <x>, offset <mu>, and parameters <lambda> and <tau>.
*/
double
esl_sxp_cdf(double x, double mu, double lambda, double tau)
{
double y = lambda * (x-mu);
double val;
if (x <= mu) return 0.;
esl_stats_IncompleteGamma(1/tau, exp(tau * log(y)), &val, NULL);
ESL_DASSERT1 (( !isnan(val)));
return val;
}
/* Function: esl_stats_ChiSquaredTest()
* Synopsis: Calculates a $\chi^2$ P-value.
* Incept: SRE, Tue Jul 19 11:39:32 2005 [St. Louis]
*
* Purpose: Calculate the probability that a chi-squared statistic
* with <v> degrees of freedom would exceed the observed
* chi-squared value <x>; return it in <ret_answer>. If
* this probability is less than some small threshold (say,
* 0.05 or 0.01), then we may reject the hypothesis we're
* testing.
*
* Args: v - degrees of freedom
* x - observed chi-squared value
* ret_answer - RETURN: P(\chi^2 > x)
*
* Returns: <eslOK> on success.
*
* Throws: <eslERANGE> if <v> or <x> are out of valid range.
* <eslENOHALT> if iterative calculation fails.
*/
int
esl_stats_ChiSquaredTest(int v, double x, double *ret_answer)
{
return esl_stats_IncompleteGamma((double)v/2, x/2, NULL, ret_answer);
}
