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binomial.go
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binomial.go
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package stat
import (
. "code.google.com/p/go-fn/fn"
)
// Probability Mass Function for the Binomial distribution
func Binomial_PMF(ρ float64, n int64) func(i int64) float64 {
return func(i int64) float64 {
p := pow(ρ, float64(i)) * pow(1-ρ, float64(n-i))
p *= Γ(float64(n+1)) / (Γ(float64(i+1)) * Γ(float64(n-i+1)))
return p
}
}
func Binomial_PMF_At(ρ float64, n, k int64) float64 {
pmf := Binomial_PMF(ρ, n)
return pmf(k)
}
// Natural logarithm of Probability Mass Function for the Binomial distribution
func Binomial_LnPMF(ρ float64, n int64) func(i int64) float64 {
return func(i int64) float64 {
p := log(ρ)*float64(i) + log(1-ρ)*float64(n-i)
p += LnΓ(float64(n+1)) - LnΓ(float64(i+1)) - LnΓ(float64(n-i+1))
return p
}
}
func NextBinomial(ρ float64, n int64) (result int64) {
for i := int64(0); i <= n; i++ {
result += NextBernoulli(ρ)
}
return
}
func Binomial(ρ float64, n int64) func() int64 {
return func() int64 { return NextBinomial(ρ, n) }
}
// Cumulative Distribution Function for the Binomial distribution, trivial implementation
func Binomial_CDF_trivial(ρ float64, n int64) func(k int64) float64 {
return func(k int64) float64 {
var p float64 = 0
var i int64
pmf := Binomial_PMF(ρ, n)
for i = 0; i <= k; i++ {
p += pmf(i)
}
return p
}
}
// Cumulative Distribution Function for the Binomial distribution
func Binomial_CDF(ρ float64, n int64) func(k int64) float64 {
return func(k int64) float64 {
p := Beta_CDF_At((float64)(n-k), (float64)(k+1), 1-ρ)
return p
}
}
func Binomial_CDF_At(ρ float64, n, k int64) float64 {
cdf := Binomial_CDF(ρ, n)
return cdf(k)
}