English: Marginal probability density functions for order statistics for a sample of size n=5 independent identically exponentially distributed random variables. Scale parameter is unity.
exponential scale parameter (characteristic life) for standard form:
eta = 1.0
exponential pdf and cdf:
pdf (t) = eta * exp (-eta * t)
cdf (t) = 1 - exp (-eta * t)
set xrange [0:5]
set yrange [0:2.3]
set format y "%0.1f"
set label 1 "i = 1" at 0.25,2.10
set label 2 "i = 2" at 0.48,1.30
set label 3 "i = 3" at 0.83,0.92
set label 4 "i = 4" at 1.25,0.68
set label 5 "i = 5" at 2.40,0.37
set style line 1 lt 1 lc rgb "#0000FF" lw 3.6
set style line 2 lt 1 lc rgb "#00FF00" lw 3.6
set style line 3 lt 1 lc rgb "#FF0000" lw 3.6
set style line 4 lt 1 lc rgb "#000000" lw 3.6
set style line 5 lt 1 lc rgb "#AA00FF" lw 3.6
plot b15 (cdf (x)) * pdf (x) with lines ls 1 title "i = 1", \
b24 (cdf (x)) * pdf (x) with lines ls 2 title "i = 2", \
b33 (cdf (x)) * pdf (x) with lines ls 3 title "i = 3", \
b42 (cdf (x)) * pdf (x) with lines ls 4 title "i = 4", \
b51 (cdf (x)) * pdf (x) with lines ls 5 title "i = 5"