#!/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
	gmt set FONT_ANNOT_PRIMARY 10p,Helvetica,black
	# 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 -Sb0.8u -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 -Sb0.8u -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 -BWS -Bxa1 -Byaf -Y2.25c
	gmt math -T-4/4/0.1 T 3 TPDF = p.txt
	gmt plot p.txt -L+yb -Glightgreen -W1p
	# 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 -Sb0.8u -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 -Sb0.8u -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 -BES -Bxa1 -Byaf -Y2.25c
	gmt math -T-4/4/0.1 T 3 TCDF = p.txt
	gmt plot p.txt -L+yb -Glightred -W1p
	# 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