/usr/include/shogun/mathematics/Statistics.h is in libshogun-dev 1.1.0-4ubuntu2.
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* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* Written (W) 2011 Heiko Strathmann
* Copyright (C) 2011 Berlin Institute of Technology and Max-Planck-Society
*
* ALGLIB Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier under GPL2+
* http://www.alglib.net/
* See method comments which functions are taken from ALGLIB (with adjustments
* for shogun)
*/
#ifndef __STATISTICS_H_
#define __STATISTICS_H_
#include <shogun/base/SGObject.h>
namespace shogun
{
/** @brief Class that contains certain functions related to statistics, such as
* the student's t distribution.
*/
class CStatistics: public CSGObject
{
public:
/** Calculates mean of given values
*
* @param values vector of values
* @return variance of given values
*/
static float64_t mean(SGVector<float64_t> values);
/** Calculates variance of given values
*
* @param values vector of values
* @return variance of given values
*/
static float64_t variance(SGVector<float64_t> values);
/** Calculates standard deviation of given values
*
* @param values vector of values
* @return standard deviation of given values
*/
static float64_t std_deviation(SGVector<float64_t> values);
/** Calculates the sample mean of a given set of samples and also computes
* the confidence interval for the actual mean for a given p-value,
* asuming that the actual variance and mean are unknown (These are
* estimated by the samples)
*
* Only for normally distributed data
*
* @param values vector of values that are used for calculations
* @param alpha actual mean lies in confidence interval with (1-alpha)*100%
* @param conf_int_low lower confidence interval border is written here
* @param conf_int_up upper confidence interval border is written here
* @return sample mean
*
*/
static float64_t confidence_intervals_mean(SGVector<float64_t> values,
float64_t alpha, float64_t& conf_int_low, float64_t& conf_int_up);
/** Student's t distribution
* Computes the integral from minus infinity to t of the Student
* For t < -2, this is the method of computation. For higher t,
* a direct method is derived from integration by parts.
* Since the function is symmetric about t=0, the area under the
* right tail of the density is found by calling the function
* with -t instead of t.
* Taken from ALGLIB under GPL2+
* @param k degrees of freedom
* @param t integral is computed from minus infinity to t
* @return described integral
*/
static float64_t student_t_distribution(int32_t k, float64_t t);
/** Functional inverse of Student's t distribution
* Given probability p, finds the argument t such that stdtr(k,t) is equal
* to p.
*
* Taken from ALGLIB under GPL2+
*
*/
static float64_t inverse_student_t_distribution(int32_t k, float64_t p);
/** Incomplete beta integral
* Returns incomplete beta integral of the arguments, evaluated
* from zero to x.
* The domain of definition is 0 <= x <= 1. In this
* implementation a and b are restricted to positive values.
* The integral is evaluated by a continued fraction expansion
* or, when b*x is small, by a power series.
*
* Taken from ALGLIB under GPL2+
*/
static float64_t incomplete_beta(float64_t a, float64_t b, float64_t x);
/** Inverse of imcomplete beta integral
* Given y, the function finds x such that
* inverse_incomplete_beta(a, b, x) = y .
* The routine performs interval halving or Newton iterations to find the
* root of inverse_incomplete_beta(a, b, x)-y=0.
*
* Taken from ALGLIB under GPL2+
*/
static float64_t inverse_incomplete_beta(float64_t a, float64_t b,
float64_t y);
/** Inverse of Normal distribution function
* Returns the argument, x, for which the area under the Gaussian
* probability density function (integrated from minus infinity to x) is
* equal to y.
*
* For small arguments 0 < y < exp(-2), the program computes
* z=sqrt(-2.0*log(y))
* then the approximation is
* x=z-log(z)/z-(1/z)P(1/z)/Q(1/z).
* There are two rational functions P/Q, one for 0 < y < exp(-32)
* and the other for y up to exp(-2). For larger arguments,
* w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
*
* Taken from ALGLIB under GPL2+
*/
static float64_t inverse_normal_distribution(float64_t y0);
/** @return object name */
inline virtual const char* get_name() const
{
return "Statistics";
}
protected:
/**
* Power series for incomplete beta integral.
* Use when b*x is small and x not too close to 1.
*
* Taken from ALGLIB under GPL2+
*/
static float64_t ibetaf_incomplete_beta_ps(float64_t a, float64_t b,
float64_t x, float64_t maxgam);
/** Continued fraction expansion #1 for incomplete beta integral
*
* Taken from ALGLIB under GPL2+
*/
static float64_t ibetaf_incomplete_beta_fe(float64_t a, float64_t b,
float64_t x, float64_t big, float64_t biginv);
/**Continued fraction expansion #2 for incomplete beta integral
*
* Taken from ALGLIB under GPL2+
*/
static float64_t ibetaf_incomplete_beta_fe2(float64_t a, float64_t b,
float64_t x, float64_t big, float64_t biginv);
};
}
#endif /* __STATISTICS_H_ */
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