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GNUplot Demonstrations
Содержание Назад Вперед
Статистические аппроксимации
#
# $Id: prob2.demo 3.38.2.6 1992/11/14 02:25:21 woo Exp $
#
# Demo Statistical Approximations version 1.1
#
# Разрешено свободное распространение только для некомерческих целей
#
# Авторское право (c) 1991, Jos van der Woude, jvdwoude@hut.nl
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pause 0 " Statistical Approximations, version 1.1"
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pause 0 " Авторское право (c) 1991, 1992, Jos van de Woude, jvdwoude@hut.nl"
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pause 0 "Разрешено свободное распространение только для некомерческих целей "
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pause 0 " Обратите внимание: содержит 10 графиков, поэтому требует времени для выполнения"
pause 0 " Нажмите Ctrl-C для выхода"
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save set "defaults.ini"
load "stat.inc"
# Распределение (нормальное приближение)
n = 25; p = 0.15
mu = n * p
sigma = sqrt(n * p * (1.0 - p))
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
ymax = 1.1 * binom(mu)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil(sigma), xmax
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 + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot binom(x), normal(x - 0.5)
изображение
 set noarrow
set nolabel
# Распределение (пуассоновское приближение)
n = 50; p = 0.1
mu = n * p
sigma = sqrt(mu)
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
ymax = 1.1 * binom(mu)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil(sigma), xmax
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 poisson approximation"
set arrow from mu + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot binom(x), poisson(x)
изображение
 set noarrow
set nolabel
# геометрическое (гамма приближение)
p = 0.3
mu = (1.0 - p) / p
sigma = sqrt(mu / p)
lambda = p
rho = 1.0 - p
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * p
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil((xmax - xmin)/ 10.0), xmax
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 + 0.5, 0 to mu + 0.5, g(mu) nohead
set arrow from mu + 0.5, g(mu + sigma) \
to mu + 0.5 + sigma, g(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, g(mu + sigma)
plot geometric(x), g(x - 0.5)
изображение
 set noarrow
set nolabel
# геометрическое (нормальное приближение)
p = 0.3
mu = (1.0 - p) / p
sigma = sqrt(mu / p)
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * p
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil((xmax - xmin)/ 10.0), xmax
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 + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot geometric(x), normal(x - 0.5)
изображение
 set noarrow
set nolabel
# гипергеометрическое (биномиальное приближение)
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 - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * hypgeo(mu) #биномиальное PDF
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k ->"
set ylabel "probability density ->"
set xtics xmin, xinc, xmax
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 binomial approximation"
set arrow from mu + 0.5, 0 to mu + 0.5, binom(mu) nohead
set arrow from mu + 0.5, binom(mu + sigma) \
to mu + 0.5 + sigma, binom(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, binom(mu + sigma)
plot hypgeo(x), binom(x)
изображение
 set noarrow
set nolabel
# гиперегеометрическое (нормальное прибилжение)
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 - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * hypgeo(mu)
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin, xinc, xmax
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 + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot hypgeo(x), normal(x - 0.5)
изображение
 set noarrow
set nolabel
# отрицательное биномиальное (гамма приближение)
r = 8; p = 0.6
mu = r * (1.0 - p) / p
sigma = sqrt(mu / p)
lambda = p
rho = r * (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 * g((rho - 1) / lambda)
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil((xmax - xmin)/ 10.0), xmax
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 + 0.5, 0 to mu + 0.5, g(mu) nohead
set arrow from mu + 0.5, g(mu + sigma) \
to mu + 0.5 + sigma, g(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, g(mu + sigma)
plot negbin(x), g(x - 0.5)
изображение
 set noarrow
set nolabel
# отрицательное биномиальное (нормальное приближение)
r = 8; p = 0.4
mu = r * (1.0 - p) / p
sigma = sqrt(mu / p)
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * negbin(mu - 1/p) # гамма PDF
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin + 0.499, ceil((xmax - xmin)/ 10.0), xmax
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 + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot negbin(x), normal(x - 0.5)
изображение
 set noarrow
set nolabel
# нормальное распределение (логистическое приближение)
mu = 1.0; sigma = 1.5
a = mu
lambda = pi / (sqrt(3.0) * sigma)
xmin = mu - 4.0 * sigma
xmax = mu + 4.0 * sigma
ymax = 1.1 * logistic(mu)
set key
set nozeroaxis
set xrange [xmin: xmax]
set yrange [0 : ymax]
set xlabel "x ->"
set ylabel "probability density ->"
set xtics xmin, (xmax - xmin)/ 10.0, xmax
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) nohead
set arrow from mu, normal(mu + sigma) \
to mu + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot logistic(x), normal(x)
изображение
 set noarrow
set nolabel
# распределение Пуассона (нормальное приближение)
mu = 5.0
sigma = sqrt(mu)
xmin = floor(mu - 4.0 * sigma)
xmin = xmin < 0 ? 0 : xmin
xmax = ceil(mu + 4.0 * sigma)
xinc = ceil((xmax - xmin) / 10)
xinc = xinc > 1 ? xinc : 1
ymax = 1.1 * poisson(mu) #распределение Пуассона
set key
set nozeroaxis
set xrange [xmin - 1 : xmax + 1]
set yrange [0 : ymax]
set xlabel "k, x ->"
set ylabel "probability density ->"
set xtics xmin, xinc, xmax
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 + 0.5, 0 to mu + 0.5, normal(mu) nohead
set arrow from mu + 0.5, normal(mu + sigma) \
to mu + 0.5 + sigma, normal(mu + sigma) nohead
set label "mu" at mu + 1, ymax / 10
set label "sigma" at mu + 1 + sigma, normal(mu + sigma)
plot poisson(x), normal(x - 0.5)
изображение
 set noarrow
set nolabel
load "defaults.ini"
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