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// Copyright ©2014 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package distuv
import (
"math"
"golang.org/x/exp/rand"
)
// UnitUniform is an instantiation of the uniform distribution with Min = 0
// and Max = 1.
var UnitUniform = Uniform{Min: 0, Max: 1}
// Uniform represents a continuous uniform distribution (https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29).
type Uniform struct {
Min float64
Max float64
Src rand.Source
}
// CDF computes the value of the cumulative density function at x.
func (u Uniform) CDF(x float64) float64 {
if x < u.Min {
return 0
}
if x > u.Max {
return 1
}
return (x - u.Min) / (u.Max - u.Min)
}
// Uniform doesn't have any of the DLogProbD? because the derivative is 0 everywhere
// except where it's undefined
// Entropy returns the entropy of the distribution.
func (u Uniform) Entropy() float64 {
return math.Log(u.Max - u.Min)
}
// ExKurtosis returns the excess kurtosis of the distribution.
func (Uniform) ExKurtosis() float64 {
return -6.0 / 5.0
}
// Uniform doesn't have Fit because it's a bad idea to fit a uniform from data.
// LogProb computes the natural logarithm of the value of the probability density function at x.
func (u Uniform) LogProb(x float64) float64 {
if x < u.Min {
return math.Inf(-1)
}
if x > u.Max {
return math.Inf(-1)
}
return -math.Log(u.Max - u.Min)
}
// MarshalParameters implements the ParameterMarshaler interface
func (u Uniform) MarshalParameters(p []Parameter) {
if len(p) != u.NumParameters() {
panic("uniform: improper parameter length")
}
p[0].Name = "Min"
p[0].Value = u.Min
p[1].Name = "Max"
p[1].Value = u.Max
}
// Mean returns the mean of the probability distribution.
func (u Uniform) Mean() float64 {
return (u.Max + u.Min) / 2
}
// Median returns the median of the probability distribution.
func (u Uniform) Median() float64 {
return (u.Max + u.Min) / 2
}
// Uniform doesn't have a mode because it's any value in the distribution
// NumParameters returns the number of parameters in the distribution.
func (Uniform) NumParameters() int {
return 2
}
// Prob computes the value of the probability density function at x.
func (u Uniform) Prob(x float64) float64 {
if x < u.Min {
return 0
}
if x > u.Max {
return 0
}
return 1 / (u.Max - u.Min)
}
// Quantile returns the inverse of the cumulative probability distribution.
func (u Uniform) Quantile(p float64) float64 {
if p < 0 || p > 1 {
panic(badPercentile)
}
return p*(u.Max-u.Min) + u.Min
}
// Rand returns a random sample drawn from the distribution.
func (u Uniform) Rand() float64 {
var rnd float64
if u.Src == nil {
rnd = rand.Float64()
} else {
rnd = rand.New(u.Src).Float64()
}
return rnd*(u.Max-u.Min) + u.Min
}
// Skewness returns the skewness of the distribution.
func (Uniform) Skewness() float64 {
return 0
}
// StdDev returns the standard deviation of the probability distribution.
func (u Uniform) StdDev() float64 {
return math.Sqrt(u.Variance())
}
// Survival returns the survival function (complementary CDF) at x.
func (u Uniform) Survival(x float64) float64 {
if x < u.Min {
return 1
}
if x > u.Max {
return 0
}
return (u.Max - x) / (u.Max - u.Min)
}
// UnmarshalParameters implements the ParameterMarshaler interface
func (u *Uniform) UnmarshalParameters(p []Parameter) {
if len(p) != u.NumParameters() {
panic("uniform: incorrect number of parameters to set")
}
if p[0].Name != "Min" {
panic("uniform: " + panicNameMismatch)
}
if p[1].Name != "Max" {
panic("uniform: " + panicNameMismatch)
}
u.Min = p[0].Value
u.Max = p[1].Value
}
// Variance returns the variance of the probability distribution.
func (u Uniform) Variance() float64 {
return 1.0 / 12.0 * (u.Max - u.Min) * (u.Max - u.Min)
}
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