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// Copyright ©2017 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"
)
// Triangle represents a triangle distribution (https://en.wikipedia.org/wiki/Triangular_distribution).
type Triangle struct {
a, b, c float64
src rand.Source
}
// NewTriangle constructs a new triangle distribution with lower limit a, upper limit b, and mode c.
// Constraints are a < b and a ≤ c ≤ b.
// This distribution is uncommon in nature, but may be useful for simulation.
func NewTriangle(a, b, c float64, src rand.Source) Triangle {
checkTriangleParameters(a, b, c)
return Triangle{a: a, b: b, c: c, src: src}
}
func checkTriangleParameters(a, b, c float64) {
if a >= b {
panic("triangle: constraint of a < b violated")
}
if a > c {
panic("triangle: constraint of a <= c violated")
}
if c > b {
panic("triangle: constraint of c <= b violated")
}
}
// CDF computes the value of the cumulative density function at x.
func (t Triangle) CDF(x float64) float64 {
switch {
case x <= t.a:
return 0
case x <= t.c:
d := x - t.a
return (d * d) / ((t.b - t.a) * (t.c - t.a))
case x < t.b:
d := t.b - x
return 1 - (d*d)/((t.b-t.a)*(t.b-t.c))
default:
return 1
}
}
// Entropy returns the entropy of the distribution.
func (t Triangle) Entropy() float64 {
return 0.5 + math.Log(t.b-t.a) - math.Ln2
}
// ExKurtosis returns the excess kurtosis of the distribution.
func (Triangle) ExKurtosis() float64 {
return -3.0 / 5.0
}
// Fit is not appropriate for Triangle, because the distribution is generally used when there is little data.
// LogProb computes the natural logarithm of the value of the probability density function at x.
func (t Triangle) LogProb(x float64) float64 {
return math.Log(t.Prob(x))
}
// Mean returns the mean of the probability distribution.
func (t Triangle) Mean() float64 {
return (t.a + t.b + t.c) / 3
}
// Median returns the median of the probability distribution.
func (t Triangle) Median() float64 {
if t.c >= (t.a+t.b)/2 {
return t.a + math.Sqrt((t.b-t.a)*(t.c-t.a)/2)
}
return t.b - math.Sqrt((t.b-t.a)*(t.b-t.c)/2)
}
// Mode returns the mode of the probability distribution.
func (t Triangle) Mode() float64 {
return t.c
}
// NumParameters returns the number of parameters in the distribution.
func (Triangle) NumParameters() int {
return 3
}
// Prob computes the value of the probability density function at x.
func (t Triangle) Prob(x float64) float64 {
switch {
case x < t.a:
return 0
case x < t.c:
return 2 * (x - t.a) / ((t.b - t.a) * (t.c - t.a))
case x == t.c:
return 2 / (t.b - t.a)
case x <= t.b:
return 2 * (t.b - x) / ((t.b - t.a) * (t.b - t.c))
default:
return 0
}
}
// Quantile returns the inverse of the cumulative probability distribution.
func (t Triangle) Quantile(p float64) float64 {
if p < 0 || p > 1 {
panic(badPercentile)
}
f := (t.c - t.a) / (t.b - t.a)
if p < f {
return t.a + math.Sqrt(p*(t.b-t.a)*(t.c-t.a))
}
return t.b - math.Sqrt((1-p)*(t.b-t.a)*(t.b-t.c))
}
// Rand returns a random sample drawn from the distribution.
func (t Triangle) Rand() float64 {
var rnd float64
if t.src == nil {
rnd = rand.Float64()
} else {
rnd = rand.New(t.src).Float64()
}
return t.Quantile(rnd)
}
// Skewness returns the skewness of the distribution.
func (t Triangle) Skewness() float64 {
n := math.Sqrt2 * (t.a + t.b - 2*t.c) * (2*t.a - t.b - t.c) * (t.a - 2*t.b + t.c)
d := 5 * math.Pow(t.a*t.a+t.b*t.b+t.c*t.c-t.a*t.b-t.a*t.c-t.b*t.c, 3.0/2.0)
return n / d
}
// StdDev returns the standard deviation of the probability distribution.
func (t Triangle) StdDev() float64 {
return math.Sqrt(t.Variance())
}
// Survival returns the survival function (complementary CDF) at x.
func (t Triangle) Survival(x float64) float64 {
return 1 - t.CDF(x)
}
// MarshalParameters implements the ParameterMarshaler interface
func (t Triangle) MarshalParameters(p []Parameter) {
if len(p) != t.NumParameters() {
panic("triangle: improper parameter length")
}
p[0].Name = "A"
p[0].Value = t.a
p[1].Name = "B"
p[1].Value = t.b
p[2].Name = "C"
p[2].Value = t.c
}
// UnmarshalParameters implements the ParameterMarshaler interface
func (t *Triangle) UnmarshalParameters(p []Parameter) {
if len(p) != t.NumParameters() {
panic("triangle: incorrect number of parameters to set")
}
if p[0].Name != "A" {
panic("triangle: " + panicNameMismatch)
}
if p[1].Name != "B" {
panic("triangle: " + panicNameMismatch)
}
if p[2].Name != "C" {
panic("triangle: " + panicNameMismatch)
}
checkTriangleParameters(p[0].Value, p[1].Value, p[2].Value)
t.a = p[0].Value
t.b = p[1].Value
t.c = p[2].Value
}
// Variance returns the variance of the probability distribution.
func (t Triangle) Variance() float64 {
return (t.a*t.a + t.b*t.b + t.c*t.c - t.a*t.b - t.a*t.c - t.b*t.c) / 18
}
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