gonum.org/v1/gonum@v0.14.0/stat/distuv/bernoulli.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  	"golang.org/x/exp/rand"
    11  )
    12  
    13  // Bernoulli represents a random variable whose value is 1 with probability p and
    14  // value of zero with probability 1-P. The value of P must be between 0 and 1.
    15  // More information at https://en.wikipedia.org/wiki/Bernoulli_distribution.
    16  type Bernoulli struct {
    17  	P   float64
    18  	Src rand.Source
    19  }
    20  
    21  // CDF computes the value of the cumulative density function at x.
    22  func (b Bernoulli) CDF(x float64) float64 {
    23  	if x < 0 {
    24  		return 0
    25  	}
    26  	if x < 1 {
    27  		return 1 - b.P
    28  	}
    29  	return 1
    30  }
    31  
    32  // Entropy returns the entropy of the distribution.
    33  func (b Bernoulli) Entropy() float64 {
    34  	if b.P == 0 || b.P == 1 {
    35  		return 0
    36  	}
    37  	q := 1 - b.P
    38  	return -b.P*math.Log(b.P) - q*math.Log(q)
    39  }
    40  
    41  // ExKurtosis returns the excess kurtosis of the distribution.
    42  func (b Bernoulli) ExKurtosis() float64 {
    43  	pq := b.P * (1 - b.P)
    44  	return (1 - 6*pq) / pq
    45  }
    46  
    47  // LogProb computes the natural logarithm of the value of the probability density function at x.
    48  func (b Bernoulli) LogProb(x float64) float64 {
    49  	if x == 0 {
    50  		return math.Log(1 - b.P)
    51  	}
    52  	if x == 1 {
    53  		return math.Log(b.P)
    54  	}
    55  	return math.Inf(-1)
    56  }
    57  
    58  // Mean returns the mean of the probability distribution.
    59  func (b Bernoulli) Mean() float64 {
    60  	return b.P
    61  }
    62  
    63  // Median returns the median of the probability distribution.
    64  func (b Bernoulli) Median() float64 {
    65  	p := b.P
    66  	switch {
    67  	case p < 0.5:
    68  		return 0
    69  	case p > 0.5:
    70  		return 1
    71  	default:
    72  		return 0.5
    73  	}
    74  }
    75  
    76  // NumParameters returns the number of parameters in the distribution.
    77  func (Bernoulli) NumParameters() int {
    78  	return 1
    79  }
    80  
    81  // Prob computes the value of the probability distribution at x.
    82  func (b Bernoulli) Prob(x float64) float64 {
    83  	if x == 0 {
    84  		return 1 - b.P
    85  	}
    86  	if x == 1 {
    87  		return b.P
    88  	}
    89  	return 0
    90  }
    91  
    92  // Quantile returns the minimum value of x from amongst all those values whose CDF value exceeds or equals p.
    93  func (b Bernoulli) Quantile(p float64) float64 {
    94  	if p < 0 || 1 < p {
    95  		panic(badPercentile)
    96  	}
    97  	if p <= 1-b.P {
    98  		return 0
    99  	}
   100  	return 1
   101  }
   102  
   103  // Rand returns a random sample drawn from the distribution.
   104  func (b Bernoulli) Rand() float64 {
   105  	var rnd float64
   106  	if b.Src == nil {
   107  		rnd = rand.Float64()
   108  	} else {
   109  		rnd = rand.New(b.Src).Float64()
   110  	}
   111  	if rnd < b.P {
   112  		return 1
   113  	}
   114  	return 0
   115  }
   116  
   117  // Skewness returns the skewness of the distribution.
   118  func (b Bernoulli) Skewness() float64 {
   119  	return (1 - 2*b.P) / math.Sqrt(b.P*(1-b.P))
   120  }
   121  
   122  // StdDev returns the standard deviation of the probability distribution.
   123  func (b Bernoulli) StdDev() float64 {
   124  	return math.Sqrt(b.Variance())
   125  }
   126  
   127  // Survival returns the survival function (complementary CDF) at x.
   128  func (b Bernoulli) Survival(x float64) float64 {
   129  	if x < 0 {
   130  		return 1
   131  	}
   132  	if x < 1 {
   133  		return b.P
   134  	}
   135  	return 0
   136  }
   137  
   138  // Variance returns the variance of the probability distribution.
   139  func (b Bernoulli) Variance() float64 {
   140  	return b.P * (1 - b.P)
   141  }