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276 lines
8.0 KiB
C++
276 lines
8.0 KiB
C++
// (C) Benjamin Sobotta 2012
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifdef _MSC_VER
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# pragma warning (disable : 4512) // assignment operator could not be generated
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# pragma warning (disable : 4127) // conditional expression is constant.
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#endif
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#include <boost/math/distributions/skew_normal.hpp>
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using boost::math::skew_normal_distribution;
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using boost::math::skew_normal;
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#include <iostream>
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#include <cmath>
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#include <utility>
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void check(const double loc, const double sc, const double sh,
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const double * const cumulants, const std::pair<double, double> qu,
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const double x, const double tpdf, const double tcdf)
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{
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using namespace boost::math;
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skew_normal D(loc, sc, sh);
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const double sk = cumulants[2] / (std::pow(cumulants[1], 1.5));
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const double kt = cumulants[3] / (cumulants[1] * cumulants[1]);
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// checks against tabulated values
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std::cout << "mean: table=" << cumulants[0] << "\tcompute=" << mean(D) << "\tdiff=" << fabs(cumulants[0]-mean(D)) << std::endl;
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std::cout << "var: table=" << cumulants[1] << "\tcompute=" << variance(D) << "\tdiff=" << fabs(cumulants[1]-variance(D)) << std::endl;
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std::cout << "skew: table=" << sk << "\tcompute=" << skewness(D) << "\tdiff=" << fabs(sk-skewness(D)) << std::endl;
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std::cout << "kur.: table=" << kt << "\tcompute=" << kurtosis_excess(D) << "\tdiff=" << fabs(kt-kurtosis_excess(D)) << std::endl;
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std::cout << "mode: table=" << "N/A" << "\tcompute=" << mode(D) << "\tdiff=" << "N/A" << std::endl;
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const double q = quantile(D, qu.first);
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const double cq = quantile(complement(D, qu.first));
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std::cout << "quantile(" << qu.first << "): table=" << qu.second << "\tcompute=" << q << "\tdiff=" << fabs(qu.second-q) << std::endl;
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// consistency
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std::cout << "cdf(quantile)=" << cdf(D, q) << "\tp=" << qu.first << "\tdiff=" << fabs(qu.first-cdf(D, q)) << std::endl;
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std::cout << "ccdf(cquantile)=" << cdf(complement(D,cq)) << "\tp=" << qu.first << "\tdiff=" << fabs(qu.first-cdf(complement(D,cq))) << std::endl;
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// PDF & CDF
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std::cout << "pdf(" << x << "): table=" << tpdf << "\tcompute=" << pdf(D,x) << "\tdiff=" << fabs(tpdf-pdf(D,x)) << std::endl;
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std::cout << "cdf(" << x << "): table=" << tcdf << "\tcompute=" << cdf(D,x) << "\tdiff=" << fabs(tcdf-cdf(D,x)) << std::endl;
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std::cout << "================================\n";
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}
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int main()
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{
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using namespace boost::math;
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double sc = 0.0,loc,sh,x,dsn,qsn,psn,p;
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std::cout << std::setprecision(20);
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double cumulants[4];
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/* R:
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> install.packages("sn")
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Warning in install.packages("sn") :
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'lib = "/usr/lib64/R/library"' is not writable
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Would you like to create a personal library
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'~/R/x86_64-unknown-linux-gnu-library/2.12'
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to install packages into? (y/n) y
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--- Please select a CRAN mirror for use in this session ---
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Loading Tcl/Tk interface ... done
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also installing the dependency ‘mnormt’
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trying URL 'http://mirrors.dotsrc.org/cran/src/contrib/mnormt_1.4-5.tar.gz'
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Content type 'application/x-gzip' length 34049 bytes (33 Kb)
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opened URL
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==================================================
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downloaded 33 Kb
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trying URL 'http://mirrors.dotsrc.org/cran/src/contrib/sn_0.4-17.tar.gz'
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Content type 'application/x-gzip' length 65451 bytes (63 Kb)
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opened URL
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==================================================
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downloaded 63 Kb
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> library(sn)
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> options(digits=22)
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> sn.cumulants(1.1, 2.2, -3.3)
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[1] -0.5799089925398568 2.0179057767837230 -2.0347951542374196
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[4] 2.2553488991015072
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> qsn(0.3, 1.1, 2.2, -3.3)
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[1] -1.180104068086876
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> psn(0.4, 1.1, 2.2, -3.3)
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[1] 0.733918618927874
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> dsn(0.4, 1.1, 2.2, -3.3)
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[1] 0.2941401101565995
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*/
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//1 st
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loc = 1.1; sc = 2.2; sh = -3.3;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = -0.5799089925398568;
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cumulants[1] = 2.0179057767837230;
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cumulants[2] = -2.0347951542374196;
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cumulants[3] = 2.2553488991015072;
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x = 0.4;
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p = 0.3;
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qsn = -1.180104068086876;
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psn = 0.733918618927874;
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dsn = 0.2941401101565995;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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/* R:
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> sn.cumulants(1.1, .02, .03)
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[1] 1.1004785154529559e+00 3.9977102296128255e-04 4.7027439329779991e-11
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[4] 1.4847542790693825e-14
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> qsn(0.01, 1.1, .02, .03)
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[1] 1.053964962950150
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> psn(1.3, 1.1, .02, .03)
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[1] 1
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> dsn(1.3, 1.1, .02, .03)
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[1] 4.754580380601393e-21
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*/
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// 2nd
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loc = 1.1; sc = .02; sh = .03;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = 1.1004785154529559e+00;
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cumulants[1] = 3.9977102296128255e-04;
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cumulants[2] = 4.7027439329779991e-11;
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cumulants[3] = 1.4847542790693825e-14;
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x = 1.3;
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p = 0.01;
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qsn = 1.053964962950150;
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psn = 1;
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dsn = 4.754580380601393e-21;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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/* R:
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> sn.cumulants(10.1, 5, -.03)
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[1] 9.980371136761052e+00 2.498568893508016e+01 -7.348037395278123e-04
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[4] 5.799821402614775e-05
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> qsn(.8, 10.1, 5, -.03)
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[1] 14.18727407491953
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> psn(-1.3, 10.1, 5, -.03)
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[1] 0.01201290665838824
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> dsn(-1.3, 10.1, 5, -.03)
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[1] 0.006254346348897927
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*/
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// 3rd
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loc = 10.1; sc = 5; sh = -.03;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = 9.980371136761052e+00;
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cumulants[1] = 2.498568893508016e+01;
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cumulants[2] = -7.348037395278123e-04;
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cumulants[3] = 5.799821402614775e-05;
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x = -1.3;
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p = 0.8;
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qsn = 14.18727407491953;
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psn = 0.01201290665838824;
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dsn = 0.006254346348897927;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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/* R:
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> sn.cumulants(-10.1, 5, 30)
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[1] -6.112791696741384 9.102169946425548 27.206345266148194 71.572537838642916
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> qsn(.8, -10.1, 5, 30)
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[1] -3.692242172277
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> psn(-1.3, -10.1, 5, 30)
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[1] 0.921592193425035
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> dsn(-1.3, -10.1, 5, 30)
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[1] 0.0339105445232089
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*/
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// 4th
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loc = -10.1; sc = 5; sh = 30;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = -6.112791696741384;
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cumulants[1] = 9.102169946425548;
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cumulants[2] = 27.206345266148194;
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cumulants[3] = 71.572537838642916;
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x = -1.3;
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p = 0.8;
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qsn = -3.692242172277;
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psn = 0.921592193425035;
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dsn = 0.0339105445232089;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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/* R:
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> sn.cumulants(0,1,5)
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[1] 0.7823901817554269 0.3878656034927102 0.2055576317962637 0.1061119471655128
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> qsn(0.5,0,1,5)
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[1] 0.674471117502844
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> psn(-0.5, 0,1,5)
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[1] 0.0002731513884140924
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> dsn(-0.5, 0,1,5)
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[1] 0.00437241570403263
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*/
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// 5th
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loc = 0; sc = 1; sh = 5;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = 0.7823901817554269;
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cumulants[1] = 0.3878656034927102;
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cumulants[2] = 0.2055576317962637;
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cumulants[3] = 0.1061119471655128;
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x = -0.5;
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p = 0.5;
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qsn = 0.674471117502844;
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psn = 0.0002731513884140924;
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dsn = 0.00437241570403263;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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/* R:
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> sn.cumulants(0,1,1e5)
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[1] 0.7978845607629713 0.3633802276960805 0.2180136141122883 0.1147706820312645
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> qsn(0.5,0,1,1e5)
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[1] 0.6744897501960818
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> psn(-0.5, 0,1,1e5)
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[1] 0
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> dsn(-0.5, 0,1,1e5)
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[1] 0
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*/
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// 6th
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loc = 0; sc = 1; sh = 1e5;
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std::cout << "location: " << loc << "\tscale: " << sc << "\tshape: " << sh << std::endl;
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cumulants[0] = 0.7978845607629713;
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cumulants[1] = 0.3633802276960805;
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cumulants[2] = 0.2180136141122883;
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cumulants[3] = 0.1147706820312645;
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x = -0.5;
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p = 0.5;
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qsn = 0.6744897501960818;
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psn = 0.;
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dsn = 0.;
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check(loc, sc, sh, cumulants, std::make_pair(p,qsn), x, dsn, psn);
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return 0;
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}
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// EOF
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