9e216da9ef
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.
334 lines
10 KiB
Gnuplot
334 lines
10 KiB
Gnuplot
#
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# $Id: prob2.dem,v 1.9 2006/06/14 03:24:09 sfeam Exp $
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#
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# Demo Statistical Approximations version 1.1
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#
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# Copyright (c) 1991, Jos van der Woude, jvdwoude@hut.nl
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# History:
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# -- --- 1991 Jos van der Woude: 1st version
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# 06 Jun 2006 Dan Sebald: Added plot methods for better visual effect.
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print " Statistical Approximations, version 1.1"
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print ""
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print " Copyright (c) 1991, 1992, Jos van de Woude, jvdwoude@hut.nl"
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print ""
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print " NOTE: contains 10 plots and consequently takes some time to run"
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print " Press Ctrl-C to exit right now"
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print ""
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pause -1 " Press Return to start demo ..."
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load "stat.inc"
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rnd(x) = floor(x+0.5)
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r_xmin = -1
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r_sigma = 4.0
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# Binomial PDF using normal approximation
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n = 25; p = 0.15
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mu = n * p
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sigma = sqrt(n * p * (1.0 - p))
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * binom(floor((n+1)*p), n, p) #mode of binomial PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "binomial PDF using normal approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot binom(rnd(x), n, p) with histeps, normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Binomial PDF using poisson approximation
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n = 50; p = 0.1
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mu = n * p
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sigma = sqrt(mu)
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * binom(floor((n+1)*p), n, p) #mode of binomial PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample (xmax - xmin + 3)
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set title "binomial PDF using poisson approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot binom(x, n, p) with histeps, poisson(x, mu) with histeps
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Geometric PDF using gamma approximation
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p = 0.3
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mu = (1.0 - p) / p
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sigma = sqrt(mu / p)
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lambda = p
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rho = 1.0 - p
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * p
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "geometric PDF using gamma approximation"
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set arrow from mu, 0 to mu, gmm(mu, rho, lambda) nohead
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set arrow from mu, gmm(mu + sigma, rho, lambda) \
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to mu + sigma, gmm(mu + sigma, rho, lambda) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, gmm(mu + sigma, rho, lambda)
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plot geometric(rnd(x),p) with histeps, gmm(x, rho, lambda)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Geometric PDF using normal approximation
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p = 0.3
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mu = (1.0 - p) / p
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sigma = sqrt(mu / p)
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * p
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "geometric PDF using normal approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot geometric(rnd(x),p) with histeps, normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Hypergeometric PDF using binomial approximation
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nn = 75; mm = 25; n = 10
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p = real(mm) / nn
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mu = n * p
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sigma = sqrt(real(nn - n) / (nn - 1.0) * n * p * (1.0 - p))
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * hypgeo(floor(mu), nn, mm, n) #mode of binom PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample (xmax - xmin + 3)
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set title "hypergeometric PDF using binomial approximation"
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set arrow from mu, 0 to mu, binom(floor(mu), n, p) nohead
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set arrow from mu, binom(floor(mu + sigma), n, p) \
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to mu + sigma, binom(floor(mu + sigma), n, p) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, binom(floor(mu + sigma), n, p)
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plot hypgeo(x, nn, mm, n) with histeps, binom(x, n, p) with histeps
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Hypergeometric PDF using normal approximation
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nn = 75; mm = 25; n = 10
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p = real(mm) / nn
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mu = n * p
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sigma = sqrt(real(nn - n) / (nn - 1.0) * n * p * (1.0 - p))
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * hypgeo(floor(mu), nn, mm, n) #mode of binom PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "hypergeometric PDF using normal approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot hypgeo(rnd(x), nn, mm, n) with histeps, normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Negative binomial PDF using gamma approximation
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r = 8; p = 0.6
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mu = r * (1.0 - p) / p
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sigma = sqrt(mu / p)
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lambda = p
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rho = r * (1.0 - p)
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * gmm((rho - 1) / lambda, rho, lambda) #mode of gamma PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "negative binomial PDF using gamma approximation"
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set arrow from mu, 0 to mu, gmm(mu, rho, lambda) nohead
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set arrow from mu, gmm(mu + sigma, rho, lambda) \
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to mu + sigma, gmm(mu + sigma, rho, lambda) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, gmm(mu + sigma, rho, lambda)
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plot negbin(rnd(x), r, p) with histeps, gmm(x, rho, lambda)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Negative binomial PDF using normal approximation
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r = 8; p = 0.4
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mu = r * (1.0 - p) / p
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sigma = sqrt(mu / p)
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * negbin(floor((r-1)*(1-p)/p), r, p) #mode of gamma PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "negative binomial PDF using normal approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot negbin(rnd(x), r, p) with histeps, normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Normal PDF using logistic approximation
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mu = 1.0; sigma = 1.5
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a = mu
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lambda = pi / (sqrt(3.0) * sigma)
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xmin = mu - r_sigma * sigma
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xmax = mu + r_sigma * sigma
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ymax = 1.1 * logistic(mu, a, lambda) #mode of logistic PDF used
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set key box
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unset zeroaxis
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set xrange [xmin: xmax]
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set yrange [0 : ymax]
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set xlabel "x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%.1f"
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set format y "%.2f"
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set sample 200
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set title "normal PDF using logistic approximation"
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set arrow from mu,0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot logistic(x, a, lambda), normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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unset arrow
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unset label
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# Poisson PDF using normal approximation
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mu = 5.0
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sigma = sqrt(mu)
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xmin = floor(mu - r_sigma * sigma)
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xmin = xmin < r_xmin ? r_xmin : xmin
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xmax = ceil(mu + r_sigma * sigma)
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ymax = 1.1 * poisson(mu, mu) #mode of poisson PDF used
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set key box
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unset zeroaxis
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set xrange [xmin - 1 : xmax + 1]
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set yrange [0 : ymax]
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set xlabel "k, x ->"
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set ylabel "probability density ->"
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set ytics 0, ymax / 10.0, ymax
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set format x "%2.0f"
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set format y "%3.2f"
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set sample 200
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set title "poisson PDF using normal approximation"
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set arrow from mu, 0 to mu, normal(mu, mu, sigma) nohead
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set arrow from mu, normal(mu + sigma, mu, sigma) \
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to mu + sigma, normal(mu + sigma, mu, sigma) nohead
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set label "mu" at mu + 0.5, ymax / 10
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set label "sigma" at mu + 0.5 + sigma, normal(mu + sigma, mu, sigma)
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plot poisson(rnd(x), mu) with histeps, normal(x, mu, sigma)
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pause -1 "Hit return to continue"
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reset
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