# (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.