diff --git a/Project.toml b/Project.toml index af12e4b7a..5483e8292 100644 --- a/Project.toml +++ b/Project.toml @@ -13,6 +13,7 @@ PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665" SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0" @@ -48,6 +49,7 @@ PDMats = "0.10, 0.11" Printf = "<0.0.1, 1" QuadGK = "2" Random = "<0.0.1, 1" +Roots = "2.2" SparseArrays = "<0.0.1, 1" SpecialFunctions = "1.2, 2" StableRNGs = "1" diff --git a/src/quantilealgs.jl b/src/quantilealgs.jl index b6eb35cbd..4733e3dc0 100644 --- a/src/quantilealgs.jl +++ b/src/quantilealgs.jl @@ -1,3 +1,5 @@ +using Roots + # Various algorithms for computing quantile function quantile_bisect(d::ContinuousUnivariateDistribution, p::Real, lx::T, rx::T) where {T<:Real} @@ -47,20 +49,8 @@ quantile_bisect(d::ContinuousUnivariateDistribution, p::Real) = # Distribution, with Application to the Inverse Gaussian Distribution # http://www.statsci.org/smyth/pubs/qinvgaussPreprint.pdf -function newton_impl(Δ, xs::T=mode(d), xrtol::Real=1e-12) where {T} - x = xs - Δ(xs) - @assert typeof(x) === T - x0 = T(xs) - while !isapprox(x, x0, atol=0, rtol=xrtol) - x0 = x - x = x0 - Δ(x0) - end - return x -end - function newton((f,df), xs::T=mode(d), xrtol::Real=1e-12) where {T} - Δ(x) = f(x)/df(x) - return newton_impl(Δ, xs, xrtol) + return find_zero((f,df), xs, Roots.Newton(), xatol=0, xrtol=xrtol, atol=0, rtol=eps(float(T)), maxiters=typemax(Int)) end function quantile_newton(d::ContinuousUnivariateDistribution, p::Real, xs::Real=mode(d), xrtol::Real=1e-12)