# # $Id: prob.demo 3.38.2.32 1992/12/04 18:33:59 woo Exp $ # # Demo Statistical Functions version 2.3 # # Permission granted to distribute freely for non-commercial purposes only # # Copyright (c) 1991, 1992 Jos van der Woude, jvdwoude@hut.nl pause 0 " Statistical Library Demo, version 2.3" pause 0 "" pause 0 " Copyright (c) 1991, 1992, Jos van de Woude, jvdwoude@hut.nl" pause 0 "Permission granted to distribute freely for non-commercial purposes only" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "" pause 0 "NOTE: contains 54 plots and consequently takes a lot of time to run" pause 0 " Press Ctrl-C to exit right now" pause -1 " Press Return to start demo ..." save set "defaults.ini" load "stat.inc" # Arcsinus PDF and CDF r = 2.0 mu = 0.0 sigma = r / sqrt2 xmin = -r xmax = r ymax = 1.1 * r #No mode set nokey set zeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 200 set title "arcsin PDF with r = 2.0" plot arcsin(x) pause -1 "Hit return to continue" set title "arcsin CDF with r = 2.0" set yrange [0 : 1.1] plot carcsin(x) pause -1 "Hit return to continue" # Beta PDF and CDF #p = 0.5; q = 0.7 #mu = p / (p + q) #sigma = sqrt(p**q) / ((p + q ) * sqrt(p + q + 1.0)) #xmin = 0.0 #xmax = 1.0 #Mode of beta PDF used #ymax = (p < 1.0 || q < 1.0) ? 2.0 : 1.1 * beta((p - 1.0)/(p + q - 2.0)) set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "beta PDF" plot [0:1] [0:5] p = 0.5, q = 0.7, beta(x) title "p = 0.5, q = 0.7", \ p = 5.0, q = 3.0, beta(x) title "p = 5.0, q = 3.0", \ p = 0.5, q = 2.5, beta(x) title "p = 0.5, q = 2.5" pause -1 "Hit return to continue" set title "incomplete beta CDF" plot [0:1] [0:1.1] p = 0.5, q = 0.7, cbeta(x) title "p = 0.5, q = 0.7", \ p = 5.0, q = 3.0, cbeta(x) title "p = 5.0, q = 3.0", \ p = 0.5, q = 2.5, cbeta(x) title "p = 0.5, q = 2.5" pause -1 "Hit return to continue" # Binomial PDF and CDF n = 25; p = 0.15 mu = n * p sigma = sqrt(n * p * (1.0 - p)) xmin = int(mu - 4.0 * sigma) xmin = xmin < 0 ? 0 : xmin xmax = int(mu + 4.0 * sigma) ymax = 1.1 * binom(mu) #Mode of normal PDF used xinc = ceil((xmax - xmin) / 10) xinc = xinc > 1 ? xinc : 1 set nokey set nozeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "k ->" set ylabel "probability density ->" set xtics xmin + 0.499, xinc, xmax set ytics 0, ymax / 10, ymax set format x "%2.0f" set format y "%3.2f" set sample (xmax - xmin) + 1 set title "binomial PDF with n = 25, p = 0.15" plot binom(x) with steps pause -1 "Hit return to continue" set title "binomial CDF with n = 25, p = 0.15" set yrange [0 : 1.1] set ytics 0, 1.1 / 10.5, 1.1 plot cbinom(x) with steps pause -1 "Hit return to continue" # Cauchy PDF and CDF #a = 0.0; b = 2.0 #cauchy PDF has no moments #xmin = a - 4.0 * b #xmax = a + 4.0 * b #ymax = 1.1 * cauchy(a) #Mode of cauchy PDF used set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "cauchy PDF" plot [-15:15] [0:0.2] a = 0, b = 2, cauchy(x) title "a = 0, b = 2", \ a = 0, b = 4, cauchy(x) title "a = 0, b = 4" pause -1 "Hit return to continue" set title "cauchy CDF" plot [-30:30] [0:1.1] a = 0, b = 2, ccauchy(x) title "a = 0, b = 2", \ a = 0, b = 4, ccauchy(x) title "a = 0, b = 4" pause -1 "Hit return to continue" # Chi-square PDF and CDF #df1 = 4.0 #mu = df1 #sigma = sqrt(2.0 * df1) #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #ymax = 1.1 * (df1 > 2.0 ? chi(df1 - 2.0) : 1.0) #Mode of chi PDF used set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "chi-square PDF" plot [0:15] [0:0.2] df1 = 4, chi(x) title "df = 4", \ df1 = 6, chi(x) title "df = 6", \ df1 = 8, chi(x) title "df = 8" pause -1 "Hit return to continue" set title "chi-square CDF" plot [0:15] [0:1.1] df1 = 4, cchi(x) title "df = 4", \ df1 = 6, cchi(x) title "df = 6", \ df1 = 8, cchi(x) title "df = 8" pause -1 "Hit return to continue" # Erlang PDF and CDF #lambda = 1.0; n = 2.0 #mu = n / lambda #sigma = sqrt(n) / lambda #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #ymax = n < 2.0 ? 1.0 : 1.1 * erlang((n - 1.0) / lambda) #Mode of erlang PDF used set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "erlang PDF" plot [0:10] [0:1] lambda = 1, n = 2, erlang(x) title "lambda = 1, n = 2", \ lambda = 2, n = 2, erlang(x) title "lambda = 2, n = 2" pause -1 "Hit return to continue" set title "erlang CDF" plot [0:10] [0:1.1] lambda = 1, n = 2, cerlang(x) title "lambda = 1, n = 2", \ lambda = 2, n = 2, cerlang(x) title "lambda = 2, n = 2" pause -1 "Hit return to continue" # Thanks to mrb2j@kelvin.seas.Virginia.EDU for telling us about this. # Extreme (Gumbel extreme value) PDF and CDF #alpha = 0.5; u = 1.0 #mu = u + (0.577215665/alpha) # Euler's constant #sigma = pi/(sqrt(6.0)*alpha) #xmin = mu - 4.0 * sigma #xmax = mu + 4.0 * sigma #ymax = 1.1 * extreme(u) #Mode of extreme PDF used set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "extreme PDF" plot [-10:10] [0:0.4] alpha = 0.5, u = 1.0, extreme(x) title "alpha = 0.5, u = 1.0", \ alpha = 1.0, u = 0.0, extreme(x) title "alpha = 1.0, u = 0.0" pause -1 "Hit return to continue" set title "extreme CDF" plot [-10:10] [0:1.1] alpha = 0.5, u = 1.0, cextreme(x) title "alpha = 0.5, u = 1.0", \ alpha = 1.0, u = 0.0, cextreme(x) title "alpha = 1.0, u = 0.0" pause -1 "Hit return to continue" # F PDF and CDF #df1 = 5.0; df2 = 9.0 #mu = df2 < 2.0 ? 1.0 : df2 / (df2 - 2.0) #sigma = df2 < 4.0 ? 1.0 : mu * sqrt(2.0 * (df1 + df2 - 2.0) / (df1 * (df2 - 4.0))) #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #Mode of F PDF used #ymax = df1 < 3.0 ? 1.0 : 1.1 * f((df1 / 2.0 - 1.0) / (df1 / 2.0 + df1 / df2)) set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0 : ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "F PDF" plot [0:4] [0:0.8] df1 = 5.0, df2 = 9.0, f(x) title "df1 = 5, df2 = 9", \ df1 = 7.0, df2 = 6.0, f(x) title "df1 = 7, df2 = 6" pause -1 "Hit return to continue" set title "F CDF" plot [0:4] [0:1.1] df1 = 5.0, df2 = 9.0, cf(x) title "df1 = 5, df2 = 9", \ df1 = 7.0, df2 = 6.0, cf(x) title "df1 = 7, df2 = 6" pause -1 "Hit return to continue" # Gamma PDF and incomplete gamma CDF #rho = 0.5; lambda = 1.0 #mu = rho / lambda #sigma = sqrt(rho) / lambda #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #ymax = rho < 1.0 ? 2.0 : 1.1 * g((rho - 1.0) / lambda) #Mode of gamma pdf used set key set zeroaxis #set xrange [xmin: xmax] #set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "gamma PDF" plot [0:5] [0:1.5] rho = 0.5, lambda = 1.0, g(x) title "rho = 0.5, lambda = 1.0", \ rho = 1.0, lambda = 1.0, g(x) title "rho = 1.0, lambda = 1.0", \ rho = 2.0, lambda = 2.0, g(x) title "rho = 2.0, lambda = 2.0" pause -1 "Hit return to continue" set title "incomplete gamma CDF (lambda == 1.0)" plot [0:5] [0:1.1] rho = 0.5, cgamma(x) title "rho = 0.5", \ rho = 1.0, cgamma(x) title "rho = 1.0", \ rho = 2.0, cgamma(x) title "rho = 2.0" pause -1 "Hit return to continue" # Geometric PDF and CDF p = 0.4 mu = (1.0 - p) / p sigma = sqrt(mu / p) xmin = int(mu - 4.0 * sigma) xmin = xmin < 0 ? 0 : xmin xmax = int(mu + 4.0 * sigma) xinc = ceil((xmax - xmin) / 10) xinc = xinc > 1 ? xinc : 1 ymax = 1.1 * geometric(mu - 1/p) #mode of gamma PDF used set nokey set nozeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "k ->" set ylabel "probability density ->" set xtics xmin + 0.499, xinc, xmax set ytics 0, ymax / 10, ymax set format x "%2.0f" set format y "%3.2f" set sample (xmax - xmin) + 1 set title "geometric PDF with p = 0.4" plot geometric(x) with steps pause -1 "Hit return to continue" set title "geometric CDF with p = 0.4" set yrange [0 : 1.1] set ytics 0, 1.1 / 10.5, 1.1 plot cgeometric(x) with steps pause -1 "Hit return to continue" # Half normal PDF and CDF mu = sqrt2invpi sigma = 1.0 s = sigma*sqrt(1.0 - 2.0/pi) xmin = 0.0 xmax = mu + 4.0 * s ymax = 1.1 * halfnormal(0) #Mode of half normal PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "half normal PDF, sigma = 1.0" plot halfnormal(x) pause -1 "Hit return to continue" set title "half normal CDF, sigma = 1.0" set yrange [0:1.1] plot chalfnormal(x) pause -1 "Hit return to continue" # Hypergeometric PDF and CPF 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 = int(mu - 4.0 * sigma) xmin = xmin < 0 ? 0 : xmin xmax = int(mu + 4.0 * sigma) xinc = ceil((xmax - xmin) / 10) xinc = xinc > 1 ? xinc : 1 ymax = 1.1 * hypgeo(mu) #mode of binomial PDF used set nokey set nozeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "k ->" set ylabel "probability density ->" set xtics xmin + 0.499, xinc, xmax set ytics 0, ymax / 10, ymax set format x "%2.0f" set format y "%3.2f" set sample (xmax - xmin) + 1 set title "hypergeometric PDF with nn = 75, mm = 25, n = 10" plot hypgeo(x) with steps pause -1 "Hit return to continue" set yrange [0 : 1.1] set ytics 0, 1.1 / 10.5, 1.1 set title "hypergeometric CDF with nn = 75, mm = 25, n = 10" plot chypgeo(x) with steps pause -1 "Hit return to continue" # Laplace PDF a = 0.0; b = 1.0 mu = a sigma = sqrt(2.0) * b xmin = mu - 4.0 * sigma xmax = mu + 4.0 * sigma ymax = 1.1 * laplace(a) #Mode of laplace PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "laplace (or double exponential) PDF with a = 0, b = 1" plot laplace(x) pause -1 "Hit return to continue" set title "laplace (or double exponential) CDF with a = 0, b = 1" set yrange [0: 1.1] plot claplace(x) pause -1 "Hit return to continue" # Logistic PDF and CDF a = 0.0; lambda = 2.0 mu = a sigma = pi / (sqrt(3.0) * lambda) xmin = mu - 4.0 * sigma xmax = mu + 4.0 * sigma ymax = 1.1 * logistic(mu) #Mode of logistic PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set nokey set zeroaxis set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "logistic PDF with a = 0, lambda = 2" plot logistic(x) pause -1 "Hit return to continue" set title "logistic CDF with a = 0, lambda = 2" set yrange [0: 1.1] plot clogistic(x) pause -1 "Hit return to continue" # Lognormal PDF and CDF mu = 1.0; sigma = 0.5 m = exp(mu + 0.5 * sigma**2) s = sqrt(exp(2.0 * mu + sigma**2) * (2.0 * exp(sigma) - 1.0)) xmin = m - 4.0 * s xmin = xmin < 0 ? 0 : xmin xmax = m + 4.0 * s ymax = 1.1 * lognormal(exp(mu - sigma**2)) #Mode of lognormal PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.2f" set sample 100 set title "lognormal PDF with mu = 1.0, sigma = 0.5" plot lognormal(x) pause -1 "Hit return to continue" set title "lognormal CDF with mu = 1.0, sigma = 0.5" set yrange [0: 1.1] plot clognormal(x) pause -1 "Hit return to continue" # Maxwell PDF #a = 0.1 #mu = 2.0 / sqrt(pi) / a #sigma = sqrt(3.0 - 8.0/pi) / a #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #ymax = 1.1 * maxwell(1.0 / a) #Mode of maxwell PDF used set key set zeroaxis #set xrange[xmin: xmax] #set yrange[0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "maxwell PDF" plot [0:6] [0:1.4] a = 1.5, maxwell(x) title "a = 1.5", \ a = 1.0, maxwell(x) title "a = 1.0", \ a = 0.5, maxwell(x) title "a = 0.5" pause -1 "Hit return to continue" set title "maxwell CDF" plot [0:6] [0:1.1] a = 1.5, cmaxwell(x) title "a = 1.5", \ a = 1.0, cmaxwell(x) title "a = 1.0", \ a = 0.5, cmaxwell(x) title "a = 0.5" pause -1 "Hit return to continue" # Negative binomial PDF and CDF r = 8; p = 0.4 mu = r * (1.0 - p) / p sigma = sqrt(mu / p) xmin = int(mu - 4.0 * sigma) xmin = xmin < 0 ? 0 : xmin xmax = int(mu + 4.0 * sigma) xinc = ceil((xmax - xmin) / 10) xinc = xinc > 1 ? xinc : 1 ymax = 1.1 * negbin(mu - 1.0/p) #mode of gamma PDF used set nokey set nozeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "k ->" set ylabel "probability density ->" set xtics xmin + 0.499, xinc, xmax set ytics 0, ymax / 10, ymax set format x "%2.0f" set format y "%3.2f" set sample (xmax - xmin) + 1 set title "negative binomial (or pascal or polya) PDF with r = 8, p = 0.4" plot negbin(x) with steps pause -1 "Hit return to continue" set yrange [0 : 1.1] set ytics 0, 1.1 / 10.5, 1.1 set title "negative binomial (or pascal or polya) CDF with r = 8, p = 0.4" plot cnegbin(x) with steps pause -1 "Hit return to continue" # Negative exponential PDF and CDF lambda = 2.0 mu = 1.0 / lambda sigma = 1.0 / lambda xmax = mu + 4.0 * sigma ymax = lambda #No mode set nokey set zeroaxis set xrange [0: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.1f" set sample 100 set title "negative exponential (or exponential) PDF with lambda = 2.0" plot nexp(x) pause -1 "Hit return to continue" set title "negative exponential (or exponential) CDF with lambda = 2.0" set yrange [0: 1.1] plot cnexp(x) pause -1 "Hit return to continue" # Normal PDF and CDF #mu = 0.0; sigma = 1.0 #xmin = mu - 4.0 * sigma #xmax = mu + 4.0 * sigma #ymax = 1.1 * normal(mu) #Mode of normal PDF used set key set zeroaxis #set xrange [xmin: xmax] #set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 100 set title "normal (also called gauss or bell-curved) PDF" plot [-4:4] [0:1] mu = 0, sigma = 1.0, normal(x) title "mu = 0, sigma = 1.0", \ mu = 2, sigma = 0.5, normal(x) title "mu = 2, sigma = 0.5", \ mu = 1, sigma = 2.0, normal(x) title "mu = 1, sigma = 2.0" pause -1 "Hit return to continue" set title "normal (also called gauss or bell-curved) CDF" plot [-4:4] [0:1.1] mu = 0, sigma = 1.0, cnormal(x) title "mu = 0, sigma = 1.0", \ mu = 2, sigma = 0.5, cnormal(x) title "mu = 2, sigma = 0.5", \ mu = 1, sigma = 2.0, cnormal(x) title "mu = 1, sigma = 2.0" pause -1 "Hit return to continue" # Pareto PDF and CDF a = 1.0; b = 3.0 mu = a * b / (b - 1.0) sigma = a * sqrt(b) / (sqrt(b - 2.0) * (b - 1.0)) xmin = mu - 4.0 * sigma xmin = xmin < 0 ? 0 : xmin xmax = mu + 4.0 * sigma ymax = 1.1 * pareto(a) #mode of pareto PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.1f" set sample 500 set title "pareto PDF with a = 1, b = 3" plot pareto(x) pause -1 "Hit return to continue" set title "pareto CDF with a = 1, b = 3" set yrange [0: 1.1] plot cpareto(x) pause -1 "Hit return to continue" # Poisson PDF and CDF mu = 4.0 sigma = sqrt(mu) xmin = int(mu - 4.0 * sigma) xmin = xmin < 0 ? 0 : xmin xmax = int(mu + 4.0 * sigma) xinc = ceil((xmax - xmin) / 10) xinc = xinc > 1 ? xinc : 1 ymax = 1.1 * poisson(mu) #mode of poisson PDF used set nokey set nozeroaxis set xrange [xmin : xmax] set yrange [0 : ymax] set xlabel "k ->" set ylabel "probability density ->" set xtics xmin + 0.499, xinc, xmax set ytics 0, ymax / 10, ymax set format x "%2.0f" set format y "%3.2f" set sample (xmax - xmin) + 1 set title "poisson PDF with mu = 4.0" plot poisson(x) with steps pause -1 "Hit return to continue" set yrange [0 : 1.1] set ytics 0, 1.1 / 10.5, 1.1 set title "poisson CDF with mu = 4.0" plot cpoisson(x) with steps pause -1 "Hit return to continue" # Rayleigh PDF and CDF lambda = 2.0 mu = 0.5 * sqrt(pi / lambda) sigma = sqrt((1.0 - pi / 4.0) / lambda) xmax = mu + 4.0 * sigma ymax = 1.1 * rayleigh(1.0 / sqrt(2.0 * lambda)) #Mode of rayleigh PDF used set nokey set zeroaxis set xrange [0: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.1f" set sample 100 set title "rayleigh PDF with lambda = 2.0" plot rayleigh(x) pause -1 "Hit return to continue" set title "rayleigh CDF with lambda = 2.0" set yrange [0: 1.1] plot crayleigh(x) pause -1 "Hit return to continue" # Sine PDF and CDF #a = 3.0; n = 2 #mu = a / 2.0 #sigma = sqrt(a * a / 3.0 * (1.0 - 3.0 / (2.0 * n * n * pi * pi)) - mu * mu) #xmin = 0.0 #xmax = a #ymax = 1.1 * 2.0 / a #Mode of sine PDF used set key set zeroaxis #set xrange [xmin: xmax] #set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.1f" set sample 100 set title "sine PDF" plot [0:2] [0:1.1] a = 2.0, n = 1, sine(x) title "a = 2.0, n = 1", \ a = 2.0, n = 3, sine(x) title "a = 2.0, n = 3" pause -1 "Hit return to continue" set title "sine CDF" plot [0:2] [0:1.1] a = 2.0, n = 1, csine(x) title "a = 2.0, n = 1", \ a = 2.0, n = 3, csine(x) title "a = 2.0, n = 3" pause -1 "Hit return to continue" # t PDF and CDF df1 = 3.0 mu = 0.0 sigma = df1 > 2.0 ? sqrt(df1 / (df1 - 2.0)) : 1.0 xmin = mu - 4.0 * sigma xmax = mu + 4.0 * sigma ymax = 1.1 * t(mu) #Mode of t PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "t PDF with df1 = 3.0" plot t(x) pause -1 "Hit return to continue" set title "t CDF with df1 = 3.0" set yrange [0: 1.1] plot ct(x) pause -1 "Hit return to continue" # Thanks to efrank@upenn5.hep.upenn.edu for telling us about this # triangular PDF and CDF m = 3.0 g = 2.0 mu = m sigma = g/sqrt(6.0) xmin = m - g xmax = m + g ymax = 1.1 * triangular(m) #Mode of triangular PDF used set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.1f" set format y "%.2f" set sample 100 set title "triangular PDF with m = 3.0, g = 2.0" plot triangular(x) pause -1 "Hit return to continue" set title "triangular CDF with m = 3.0, g = 2.0" set yrange [0: 1.1] plot ctriangular(x) pause -1 "Hit return to continue" # Uniform PDF and CDF a = -2.0; b= 2.0 mu = (a + b) / 2.0 sigma = (b - a) / sqrt(12.0) xmin = a xmax = b ymax = 1.1 * uniform(mu) #No mode set nokey set zeroaxis set xrange [xmin: xmax] set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.2f" set sample 100 set title "uniform PDF with a = -2.0, b = 2.0" plot uniform(x) pause -1 "Hit return to continue" set title "uniform CDF with a = -2.0, b = 2.0" set yrange [0: 1.1] plot cuniform(x) pause -1 "Hit return to continue" # Weibull PDF and CDF #lambda = 1.0; n = 1.5 #mu = lambda**(-1.0 / n) * gamma(1.0 / n) / n #sigma = sqrt(2.0 * lambda**(-2.0 / n) * gamma(2.0 / n) / n - mu * mu) #xmin = mu - 4.0 * sigma #xmin = xmin < 0 ? 0 : xmin #xmax = mu + 4.0 * sigma #Mode of weibull PDF used #ymax = 1.1 * (n > 1.0 ? weibull(((n - 1.0) / (lambda * n))**(1.0 / n)) : 2.0) set key set zeroaxis #set xrange [xmin : xmax] #set yrange [0: ymax] set xlabel "x ->" set ylabel "probability density ->" set xtics set ytics set format x "%.2f" set format y "%.1f" set sample 100 set title "weibull PDF" plot [0:2] [0:1.5] lambda = 1, n = 0.5, weibull(x) title "lambda = 1, n = 0.5", \ lambda = 1, n = 1.0, weibull(x) title "lambda = 1, n = 1.0", \ lambda = 1, n = 2.0, weibull(x) title "lambda = 1, n = 2.0", \ lambda = 3, n = 2.0, weibull(x) title "lambda = 3, n = 2.0" pause -1 "Hit return to continue" set title "weibull CDF" plot [0:3] [0:1.2] lambda = 1, n = 0.5, cweibull(x) title "lambda = 1, n = 0.5", \ lambda = 1, n = 1.0, cweibull(x) title "lambda = 1, n = 1.0", \ lambda = 1, n = 2.0, cweibull(x) title "lambda = 1, n = 2.0", \ lambda = 3, n = 2.0, cweibull(x) title "lambda = 3, n = 2.0" load "defaults.ini"