github.com/gopherd/gonum@v0.0.4/stat/distuv/chisquared.go (about)

     1  // Copyright ©2016 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package distuv
     6  
     7  import (
     8  	"math"
     9  
    10  	"math/rand"
    11  
    12  	"github.com/gopherd/gonum/mathext"
    13  )
    14  
    15  // ChiSquared implements the χ² distribution, a one parameter distribution
    16  // with support on the positive numbers.
    17  //
    18  // The density function is given by
    19  //  1/(2^{k/2} * Γ(k/2)) * x^{k/2 - 1} * e^{-x/2}
    20  // It is a special case of the Gamma distribution, Γ(k/2, 1/2).
    21  //
    22  // For more information, see https://en.wikipedia.org/wiki/Chi-squared_distribution.
    23  type ChiSquared struct {
    24  	// K is the shape parameter, corresponding to the degrees of freedom. Must
    25  	// be greater than 0.
    26  	K float64
    27  
    28  	Src rand.Source
    29  }
    30  
    31  // CDF computes the value of the cumulative density function at x.
    32  func (c ChiSquared) CDF(x float64) float64 {
    33  	return mathext.GammaIncReg(c.K/2, x/2)
    34  }
    35  
    36  // ExKurtosis returns the excess kurtosis of the distribution.
    37  func (c ChiSquared) ExKurtosis() float64 {
    38  	return 12 / c.K
    39  }
    40  
    41  // LogProb computes the natural logarithm of the value of the probability
    42  // density function at x.
    43  func (c ChiSquared) LogProb(x float64) float64 {
    44  	if x < 0 {
    45  		return math.Inf(-1)
    46  	}
    47  	lg, _ := math.Lgamma(c.K / 2)
    48  	return (c.K/2-1)*math.Log(x) - x/2 - (c.K/2)*math.Ln2 - lg
    49  }
    50  
    51  // Mean returns the mean of the probability distribution.
    52  func (c ChiSquared) Mean() float64 {
    53  	return c.K
    54  }
    55  
    56  // Mode returns the mode of the distribution.
    57  func (c ChiSquared) Mode() float64 {
    58  	return math.Max(c.K-2, 0)
    59  }
    60  
    61  // NumParameters returns the number of parameters in the distribution.
    62  func (c ChiSquared) NumParameters() int {
    63  	return 1
    64  }
    65  
    66  // Prob computes the value of the probability density function at x.
    67  func (c ChiSquared) Prob(x float64) float64 {
    68  	return math.Exp(c.LogProb(x))
    69  }
    70  
    71  // Rand returns a random sample drawn from the distribution.
    72  func (c ChiSquared) Rand() float64 {
    73  	return Gamma{c.K / 2, 0.5, c.Src}.Rand()
    74  }
    75  
    76  // Quantile returns the inverse of the cumulative distribution function.
    77  func (c ChiSquared) Quantile(p float64) float64 {
    78  	if p < 0 || p > 1 {
    79  		panic(badPercentile)
    80  	}
    81  	return mathext.GammaIncRegInv(0.5*c.K, p) * 2
    82  }
    83  
    84  // StdDev returns the standard deviation of the probability distribution.
    85  func (c ChiSquared) StdDev() float64 {
    86  	return math.Sqrt(c.Variance())
    87  }
    88  
    89  // Survival returns the survival function (complementary CDF) at x.
    90  func (c ChiSquared) Survival(x float64) float64 {
    91  	if x < 0 {
    92  		return 1
    93  	}
    94  	return mathext.GammaIncRegComp(0.5*c.K, 0.5*x)
    95  }
    96  
    97  // Variance returns the variance of the probability distribution.
    98  func (c ChiSquared) Variance() float64 {
    99  	return 2 * c.K
   100  }