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Summary
| Description |
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. |
| Date | |
| Source | Own work |
| Author | Lovibond |
Gnuplot code:
- Density functions for exponential order statistics (n=5)
set terminal svg size 1300 975 fname "DejaVu Sans" fsize 20 set output "OrderStatistics_Exponential_PDF.svg"
set termopt enhanced
unset key
set xlabel "x" font "DejaVu Sans, 24" set ylabel "f_{X_{(i)}}(x)" font "DejaVu Sans, 24"
- beta density functions:
b15 (t) = 5 * (1-t)**4 b24 (t) = 20 * t * (1-t)**3 b33 (t) = 30 * (t * (1-t))**2 b42 (t) = 20 * t**3 * (1-t) b51 (t) = 5 * t**4
- 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"
Licensing
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:48, 21 May 2013 | | 1,300 × 975 (40 KB) | Lovibond | User created page with UploadWizard |
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