(50) Probability distributions
This example presents visually the various probability distributions available in gmtmath (as well as grdmath). We evaluate and display both the probability density function (pdf) and the cumulative distribution function (cdf) for each case. The left column shows the density functions while the right column shows the cumulative functions. In addition to the distributions you can also use gmtmath to evaluate critical values for the distributions for chosen confidence levels.
#!/usr/bin/env bash
# GMT EXAMPLE 50
#
# Purpose: Illustrate different statistical distributions in gmtmath
# GMT modules: math, set, plot, text
#
gmt begin ex50
# Left column have all the PDFs
# Binomial distribution
gmt math -T0/8/1 0.25 8 T BPDF = p.txt
gmt plot -R-0.6/8.6/0/0.35 -JX7.5c/1.25c -Glightgreen p.txt -Sb0.8q -W0.5p -BWS -Bxa1 -Byaf
# Poisson distribution
gmt math -T0/8/1 T 2 PPDF = p.txt
gmt plot -R-0.6/8.6/0/0.3 -Glightgreen p.txt -Sb0.8q -W0.5p -BWS -Bxa1 -Byaf -Y2.25c
# Plot normal distribution
gmt math -T-4/4/0.1 T ZPDF = p.txt
gmt plot -R-4/4/0/0.4 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot t distribution
gmt plot -R-4/4/0/0.4 p.txt -W1p,lightgray -Y2.25c
gmt math -T-4/4/0.1 T 3 TPDF = p.txt
gmt plot p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf
# Plot F distribution
gmt math -T0/6/0.02 T 20 12 FPDF = p.txt
gmt plot -R0/6/0/1.02 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot Laplace distribution
gmt math -T-4/4/0.1 T LPDF = p.txt
gmt plot -R-4/4/0/0.5 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot Exponential distribution
gmt math -T0/4/0.1 T 2 EPDF = p.txt
gmt plot -R0/4/0/2.0 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot Rayleigh distribution
gmt math -T0/6/0.1 T RPDF = p.txt
gmt plot -R0/6/0/0.7 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot Weibull distribution
gmt math -T0/6/0.1 T 1 1.5 WPDF = p.txt
gmt plot -R0/6/0/0.8 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Plot Chi-squared distribution
gmt math -T0/12/0.1 T 4 CHI2PDF = p.txt
gmt plot -R0/12/0/0.20 p.txt -L+yb -Glightgreen -W1p -BWS -Bxa1 -Byaf -Y2.25c
# Right column has all the CDF
# Plot binomial cumulative distribution
gmt math -T0/8/1 0.25 8 T BCDF = p.txt
gmt plot -R-0.6/8.6/0/1.02 -Glightred p.txt -Sb0.8q -W0.5p -BES -Bxa1 -Byaf -X9c -Y-8.1i
# Plot Poisson cumulative distribution
gmt math -T0/8/1 T 2 PCDF = p.txt
gmt plot -R-0.6/8.6/0/1.02 -Glightred p.txt -Sb0.8q -W0.5p -BES -Bxa1 -Byaf -Y2.25c
# Plot normal cumulative distribution
gmt math -T-4/4/0.1 T ZCDF = p.txt
gmt plot -R-4/4/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot t cumulative distribution
gmt plot -R-4/4/0/1.02 p.txt -W1p,lightgray -Y2.25c
gmt math -T-4/4/0.1 T 3 TCDF = p.txt
gmt plot p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf
# Plot F cumulative distribution
gmt math -T0/6/0.02 T 20 12 FCDF = p.txt
gmt plot -R0/6/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot Laplace cumulative distribution
gmt math -T-4/4/0.1 T LCDF = p.txt
gmt plot -R-4/4/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot Exponential cumulative distribution
gmt math -T0/4/0.1 T 2 ECDF = p.txt
gmt plot -R0/4/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot Rayleigh cumulative distribution
gmt math -T0/6/0.1 T RCDF = p.txt
gmt plot -R0/6/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot Weibull cumulative distribution
gmt math -T0/6/0.1 T 1 1.5 WCDF = p.txt
gmt plot -R0/6/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
# Plot Chi-squared cumulative distribution
gmt math -T0/12/0.1 T 4 CHI2CDF = p.txt
gmt plot -R0/12/0/1.02 p.txt -L+yb -Glightred -W1p -BES -Bxa1 -Byaf -Y2.25c
gmt text -R0/17/0/3 -Jx1c -N -X-9c -F+f18p+cTC+t"Probability @;lightgreen;Density@;; and @;lightred;Cumulative@;; Distribution Functions"
gmt text -R0/17/0/25 -F+f14p,Times-Italic+jTC -Dj0.9c -N -Y-20.25c <<- EOF
8.3 2.25 Binomial P@-8,0.25@-
8.3 4.50 Poisson P(@~l=2@~)
8.3 6.75 Normal P(z)
8.3 9.00 Student t(@~n=3@~)
8.3 11.25 F(@~n@-1@-=20, n@-2@- = 12@~)
8.3 13.50 Laplace P(z)
8.3 15.75 Exponential P(@~l=2@~)
8.3 18.00 Rayleigh P(z)
8.3 20.25 Weibull P(z,1,1.5)
8.3 22.50 @~c@~@+2@+(z,@~n=4@~)
EOF
rm -f p.txt
gmt end show
Probability distributions.