prob.dem

智能画图软件

# 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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
unset key
set zeroaxis
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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 zeroaxis
#set xrange[xmin: xmax]
#set yrange[0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
set format x "%.1f"
set format y "%.1f"
set sample 100
set title "maxwell PDF"
set key right top box
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"
set key right bottom box
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
unset key
unset zeroaxis
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
unset key
set zeroaxis
set xrange [0: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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 zeroaxis
#set xrange [xmin: xmax]
#set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
set format x "%.1f"
set format y "%.1f"
set sample 100
set title "normal (also called gauss or bell-curved) PDF"
set key left top box
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"
set key left top box
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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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
unset key
unset zeroaxis
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
unset key
set zeroaxis
set xrange [0: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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 zeroaxis
#set xrange [xmin: xmax]
#set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
set format x "%.2f"
set format y "%.1f"
set sample 100
set title "sine PDF"
set key bottom outside
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"
set key top left
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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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 [e-mail] 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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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
unset key
set zeroaxis
set xrange [xmin: xmax]
set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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 on
set zeroaxis
#set xrange [xmin : xmax]
#set yrange [0: ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics autofreq
set ytics autofreq
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"
pause -1 "Hit return to continue"
reset