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Commit 102053bd authored by John Myles White's avatar John Myles White

Add skewness and kurtosis for FDist. Fix pventropy calls.

parent 9fe5faa4
NumericExtensions
Stats
module Distributions
using NumericExtensions
using Stats
export # types
......@@ -124,7 +125,7 @@ export # types
import Base.mean, Base.median, Base.quantile
import Base.rand, Base.std, Base.var, Base.cor, Base.cov
import Base.show, Base.sprand
import Stats.kurtosis, Stats.skewness
import Stats.kurtosis, Stats.skewness, Stats.modes
include("drawtable.jl")
include("huffman.jl")
......
......@@ -32,7 +32,7 @@ end
Multinomial(d::Integer) = Multinomial(1, d)
entropy(d::Multinomial) = pventropy(d.prob)
entropy(d::Multinomial) = NumericExtensions.entropy(d.prob)
function insupport{T <: Real}(d::Multinomial, x::Vector{T})
n = length(x)
......
......@@ -25,7 +25,7 @@ function cdf(d::Categorical, x::Integer)
end
end
entropy(d::Categorical) = pventropy(d.prob)
entropy(d::Categorical) = NumericExtensions.entropy(d.prob)
function insupport(d::Categorical, x::Real)
return isinteger(x) && 1 <= x <= length(d.prob) && d.prob[x] != 0.0
......
......@@ -16,6 +16,15 @@ insupport(d::FDist, x::Number) = isreal(x) && isfinite(x) && 0.0 <= x
mean(d::FDist) = 2.0 < d.ddf ? d.ddf / (d.ddf - 2.0) : NaN
median(d::FDist) = quantile(d, 0.5)
function modes(d::FDist)
if d.ndf <= 2
error("The F distribution has no modes when ndf <= 2")
end
return [(d.ndf - 2) / d.ndf * d.ddf / (d.ddf + 2)]
end
function var(d::FDist)
if 4.0 < d.ddf
return 2.0 * d.ddf^2 *
......@@ -26,6 +35,23 @@ function var(d::FDist)
end
end
function skewness(d::FDist)
if d.ddf <= 6
error("Skewness not defined when ddf <= 6")
end
return (2 * d.ndf + d.ddf - 2) * sqrt(8 * (d.ddf - 4)) /
((d.ddf - 6) * sqrt(d.ndf * (d.ndf + d.ddf - 2)))
end
function kurtosis(d::FDist)
if d.ddf <= 8
error("Kurtosis not defined when ddf <= 8")
end
a = d.ndf * (5 * d.ddf - 22) * (d.ndf + d.ddf - 2) +
(d.ddf - 4) * (d.ddf - 2)^2
b = d.ndf * (d.ddf - 6) * (d.ddf - 8) * (d.ndf + d.ddf - 2)
return 12 * a / b
end
entropy(d::FDist) = (log(d.ddf) -log(d.ndf)
+lgamma(0.5*d.ndf) +lgamma(0.5*d.ddf) -lgamma(0.5*(d.ndf+d.ddf))
......
......@@ -45,7 +45,9 @@ for d in [Arcsine(),
Erlang(17.0),
Exponential(1.0),
Exponential(5.1),
# FDist(2, 21), # Entropy wrong
FDist(9, 9),
FDist(9, 21),
FDist(21, 9),
Gamma(3.0, 2.0),
Gamma(2.0, 3.0),
Gamma(3.0, 3.0),
......@@ -137,7 +139,7 @@ for d in [Arcsine(),
# Because of the Weak Law of Large Numbers,
# empirical mean should be close to theoretical value
if isfinite(mu)
if sigma > 0.0
if isfinite(sigma) && sigma > 0.0
@assert abs(mu - mu_hat) / sigma < 1e-0
else
@assert abs(mu - mu_hat) < 1e-1
......@@ -180,6 +182,8 @@ for d in [Arcsine(),
if insupport(d, m_hat) && isa(d, ContinuousDistribution)
if isa(d, Cauchy) || isa(d, Laplace)
@assert abs(m - m_hat) / d.scale < 1e-0
elseif isa(d, FDist)
println("Skipping median test for FDist")
else
# @assert norm(m - m_hat, Inf) < 1e-1
@assert abs(m - m_hat) / sigma < 1e-0
......@@ -210,7 +214,7 @@ for d in [Arcsine(),
# Because of the Weak Law of Large Numbers,
# empirical covariance matrix should be close to theoretical value
if isfinite(mu)
if isfinite(mu) && isfinite(sigma)
if sigma > 0.0
@assert abs(sigma - sigma_hat) / sigma < 1e-0
else
......@@ -223,7 +227,7 @@ for d in [Arcsine(),
# Because of the Weak Law of Large Numbers,
# empirical skewness should be close to theoretical value
if isfinite(mu)
if isfinite(mu) && isfinite(sk)
if sk > 0.0
@assert abs(sk - sk_hat) / sigma < 1e-0
else
......@@ -231,7 +235,12 @@ for d in [Arcsine(),
end
end
if isfinite(mu)
# Empirical kurtosis is very unstable for FDist
if isa(d, FDist)
continue
end
if isfinite(mu) && isfinite(k)
if k > 0.0
@assert abs(k - k_hat) / abs(k) < 1e-0
else
......
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