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diff --git a/tests/examplefiles/test.plot b/tests/examplefiles/test.plot new file mode 100644 index 00000000..cef0f908 --- /dev/null +++ b/tests/examplefiles/test.plot @@ -0,0 +1,333 @@ +# +# $Id: prob2.dem,v 1.9 2006/06/14 03:24:09 sfeam Exp $ +# +# Demo Statistical Approximations version 1.1 +# +# Copyright (c) 1991, Jos van der Woude, jvdwoude@hut.nl + +# History: +# -- --- 1991 Jos van der Woude: 1st version +# 06 Jun 2006 Dan Sebald: Added plot methods for better visual effect. + +print "" +print "" +print "" +print "" +print "" +print "" +print " Statistical Approximations, version 1.1" +print "" +print " Copyright (c) 1991, 1992, Jos van de Woude, jvdwoude@hut.nl" +print "" +print "" +print "" +print "" +print "" +print "" +print "" +print "" +print "" +print "" +print "" +print " NOTE: contains 10 plots and consequently takes some time to run" +print " Press Ctrl-C to exit right now" +print "" +pause -1 " Press Return to start demo ..." + +load "stat.inc" +rnd(x) = floor(x+0.5) +r_xmin = -1 +r_sigma = 4.0 + +# Binomial PDF using normal approximation +n = 25; p = 0.15 +mu = n * p +sigma = sqrt(n * p * (1.0 - p)) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * binom(floor((n+1)*p), n, p) #mode of binomial PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "binomial PDF using normal approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot binom(rnd(x), n, p) with histeps, normal(x, mu, sigma) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Binomial PDF using poisson approximation +n = 50; p = 0.1 +mu = n * p +sigma = sqrt(mu) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * binom(floor((n+1)*p), n, p) #mode of binomial PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample (xmax - xmin + 3) +set title "binomial PDF using poisson approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot binom(x, n, p) with histeps, poisson(x, mu) with histeps +pause -1 "Hit return to continue" +unset arrow +unset label + +# Geometric PDF using gamma approximation +p = 0.3 +mu = (1.0 - p) / p +sigma = sqrt(mu / p) +lambda = p +rho = 1.0 - p +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * p +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "geometric PDF using gamma approximation" +set arrow from mu, 0 to mu, gmm(mu, rho, lambda) nohead +set arrow from mu, gmm(mu + sigma, rho, lambda) \ + to mu + sigma, gmm(mu + sigma, rho, lambda) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, gmm(mu + sigma, rho, lambda) +plot geometric(rnd(x),p) with histeps, gmm(x, rho, lambda) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Geometric PDF using normal approximation +p = 0.3 +mu = (1.0 - p) / p +sigma = sqrt(mu / p) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * p +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "geometric PDF using normal approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot geometric(rnd(x),p) with histeps, normal(x, mu, sigma) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Hypergeometric PDF using binomial approximation +nn = 75; mm = 25; n = 10 +p = real(mm) / nn +mu = n * p +sigma = sqrt(real(nn - n) / (nn - 1.0) * n * p * (1.0 - p)) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * hypgeo(floor(mu), nn, mm, n) #mode of binom PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample (xmax - xmin + 3) +set title "hypergeometric PDF using binomial approximation" +set arrow from mu, 0 to mu, binom(floor(mu), n, p) nohead +set arrow from mu, binom(floor(mu + sigma), n, p) \ + to mu + sigma, binom(floor(mu + sigma), n, p) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, binom(floor(mu + sigma), n, p) +plot hypgeo(x, nn, mm, n) with histeps, binom(x, n, p) with histeps +pause -1 "Hit return to continue" +unset arrow +unset label + +# Hypergeometric PDF using normal approximation +nn = 75; mm = 25; n = 10 +p = real(mm) / nn +mu = n * p +sigma = sqrt(real(nn - n) / (nn - 1.0) * n * p * (1.0 - p)) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * hypgeo(floor(mu), nn, mm, n) #mode of binom PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "hypergeometric PDF using normal approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot hypgeo(rnd(x), nn, mm, n) with histeps, normal(x, mu, sigma) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Negative binomial PDF using gamma approximation +r = 8; p = 0.6 +mu = r * (1.0 - p) / p +sigma = sqrt(mu / p) +lambda = p +rho = r * (1.0 - p) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * gmm((rho - 1) / lambda, rho, lambda) #mode of gamma PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "negative binomial PDF using gamma approximation" +set arrow from mu, 0 to mu, gmm(mu, rho, lambda) nohead +set arrow from mu, gmm(mu + sigma, rho, lambda) \ + to mu + sigma, gmm(mu + sigma, rho, lambda) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, gmm(mu + sigma, rho, lambda) +plot negbin(rnd(x), r, p) with histeps, gmm(x, rho, lambda) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Negative binomial PDF using normal approximation +r = 8; p = 0.4 +mu = r * (1.0 - p) / p +sigma = sqrt(mu / p) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * negbin(floor((r-1)*(1-p)/p), r, p) #mode of gamma PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "negative binomial PDF using normal approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot negbin(rnd(x), r, p) with histeps, normal(x, mu, sigma) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Normal PDF using logistic approximation +mu = 1.0; sigma = 1.5 +a = mu +lambda = pi / (sqrt(3.0) * sigma) +xmin = mu - r_sigma * sigma +xmax = mu + r_sigma * sigma +ymax = 1.1 * logistic(mu, a, lambda) #mode of logistic PDF used +set key box +unset zeroaxis +set xrange [xmin: xmax] +set yrange [0 : ymax] +set xlabel "x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%.1f" +set format y "%.2f" +set sample 200 +set title "normal PDF using logistic approximation" +set arrow from mu,0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot logistic(x, a, lambda), normal(x, mu, sigma) +pause -1 "Hit return to continue" +unset arrow +unset label + +# Poisson PDF using normal approximation +mu = 5.0 +sigma = sqrt(mu) +xmin = floor(mu - r_sigma * sigma) +xmin = xmin < r_xmin ? r_xmin : xmin +xmax = ceil(mu + r_sigma * sigma) +ymax = 1.1 * poisson(mu, mu) #mode of poisson PDF used +set key box +unset zeroaxis +set xrange [xmin - 1 : xmax + 1] +set yrange [0 : ymax] +set xlabel "k, x ->" +set ylabel "probability density ->" +set ytics 0, ymax / 10.0, ymax +set format x "%2.0f" +set format y "%3.2f" +set sample 200 +set title "poisson PDF using normal approximation" +set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead +set arrow from mu, normal(mu + sigma, mu, sigma) \ + to mu + sigma, normal(mu + sigma, mu, sigma) nohead +set label "mu" at mu + 0.5, ymax / 10 +set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma) +plot poisson(rnd(x), mu) with histeps, normal(x, mu, sigma) +pause -1 "Hit return to continue" +reset |