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

     1  // Copyright ©2018 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  
    13  // GumbelRight implements the right-skewed Gumbel distribution, a two-parameter
    14  // continuous distribution with support over the real numbers. The right-skewed
    15  // Gumbel distribution is also sometimes known as the Extreme Value distribution.
    16  //
    17  // The right-skewed Gumbel distribution has density function
    18  //  1/beta * exp(-(z + exp(-z)))
    19  //  z = (x - mu)/beta
    20  // Beta must be greater than 0.
    21  //
    22  // For more information, see https://en.wikipedia.org/wiki/Gumbel_distribution.
    23  type GumbelRight struct {
    24  	Mu   float64
    25  	Beta float64
    26  	Src  rand.Source
    27  }
    28  
    29  func (g GumbelRight) z(x float64) float64 {
    30  	return (x - g.Mu) / g.Beta
    31  }
    32  
    33  // CDF computes the value of the cumulative density function at x.
    34  func (g GumbelRight) CDF(x float64) float64 {
    35  	z := g.z(x)
    36  	return math.Exp(-math.Exp(-z))
    37  }
    38  
    39  // Entropy returns the differential entropy of the distribution.
    40  func (g GumbelRight) Entropy() float64 {
    41  	return math.Log(g.Beta) + eulerMascheroni + 1
    42  }
    43  
    44  // ExKurtosis returns the excess kurtosis of the distribution.
    45  func (g GumbelRight) ExKurtosis() float64 {
    46  	return 12.0 / 5
    47  }
    48  
    49  // LogProb computes the natural logarithm of the value of the probability density function at x.
    50  func (g GumbelRight) LogProb(x float64) float64 {
    51  	z := g.z(x)
    52  	return -math.Log(g.Beta) - z - math.Exp(-z)
    53  }
    54  
    55  // Mean returns the mean of the probability distribution.
    56  func (g GumbelRight) Mean() float64 {
    57  	return g.Mu + g.Beta*eulerMascheroni
    58  }
    59  
    60  // Median returns the median of the Gumbel distribution.
    61  func (g GumbelRight) Median() float64 {
    62  	return g.Mu - g.Beta*math.Log(math.Ln2)
    63  }
    64  
    65  // Mode returns the mode of the normal distribution.
    66  func (g GumbelRight) Mode() float64 {
    67  	return g.Mu
    68  }
    69  
    70  // NumParameters returns the number of parameters in the distribution.
    71  func (GumbelRight) NumParameters() int {
    72  	return 2
    73  }
    74  
    75  // Prob computes the value of the probability density function at x.
    76  func (g GumbelRight) Prob(x float64) float64 {
    77  	return math.Exp(g.LogProb(x))
    78  }
    79  
    80  // Quantile returns the inverse of the cumulative probability distribution.
    81  func (g GumbelRight) Quantile(p float64) float64 {
    82  	if p < 0 || 1 < p {
    83  		panic(badPercentile)
    84  	}
    85  	return g.Mu - g.Beta*math.Log(-math.Log(p))
    86  }
    87  
    88  // Rand returns a random sample drawn from the distribution.
    89  func (g GumbelRight) Rand() float64 {
    90  	var rnd float64
    91  	if g.Src == nil {
    92  		rnd = rand.ExpFloat64()
    93  	} else {
    94  		rnd = rand.New(g.Src).ExpFloat64()
    95  	}
    96  	return g.Mu - g.Beta*math.Log(rnd)
    97  }
    98  
    99  // Skewness returns the skewness of the distribution.
   100  func (GumbelRight) Skewness() float64 {
   101  	return 12 * math.Sqrt(6) * apery / (math.Pi * math.Pi * math.Pi)
   102  }
   103  
   104  // StdDev returns the standard deviation of the probability distribution.
   105  func (g GumbelRight) StdDev() float64 {
   106  	return (math.Pi / math.Sqrt(6)) * g.Beta
   107  }
   108  
   109  // Survival returns the survival function (complementary CDF) at x.
   110  func (g GumbelRight) Survival(x float64) float64 {
   111  	return 1 - g.CDF(x)
   112  }
   113  
   114  // Variance returns the variance of the probability distribution.
   115  func (g GumbelRight) Variance() float64 {
   116  	return math.Pi * math.Pi * g.Beta * g.Beta / 6
   117  }