Hana 9e216da9ef go.mod: add go.mod and move pygments to third_party
After go1.16, go will use module mode by default,
even when the repository is checked out under GOPATH
or in a one-off directory. Add go.mod, go.sum to keep
this repo buildable without opting out of the module
mode.

> go mod init github.com/mmcgrana/gobyexample
> go mod tidy
> go mod vendor

In module mode, the 'vendor' directory is special
and its contents will be actively maintained by the
go command. pygments aren't the dependency the go will
know about, so it will delete the contents from vendor
directory. Move it to `third_party` directory now.

And, vendor the blackfriday package.

Note: the tutorial contents are not affected by the
change in go1.16 because all the examples in this
tutorial ask users to run the go command with the
explicit list of files to be compiled (e.g.
`go run hello-world.go` or `go build command-line-arguments.go`).
When the source list is provided, the go command does
not have to compute the build list and whether it's
running in GOPATH mode or module mode becomes irrelevant.
2021-02-15 16:45:26 -05:00

334 lines
10 KiB
Gnuplot

#
# $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