Annotation of OpenXM_contrib/gnuplot/demo/prob.dem, Revision 1.1.1.1
1.1 maekawa 1: #
2: # $Id: prob.dem,v 1.4 1996/12/09 15:58:09 drd Exp $
3: #
4: # Demo Statistical Functions version 2.3
5: #
6: # Permission granted to distribute freely for non-commercial purposes only
7: #
8: # Copyright (c) 1991, 1992 Jos van der Woude, jvdwoude@hut.nl
9:
10: print " Statistical Library Demo, version 2.3"
11: print "\n Copyright (c) 1991, 1992, Jos van de Woude, jvdwoude@hut.nl"
12: print "Permission granted to distribute freely for non-commercial purposes only"
13: print "\n\n\n\n\n\n\n"
14: print "NOTE: contains 54 plots and consequently takes a lot of time to run"
15: print " Press Ctrl-C to exit right now"
16: pause -1 " Press Return to start demo ..."
17:
18: load "stat.inc"
19:
20: # Arcsinus PDF and CDF
21: r = 2.0
22: mu = 0.0
23: sigma = r / sqrt2
24: xmin = -r
25: xmax = r
26: ymax = 1.1 * r #No mode
27: set nokey
28: set zeroaxis
29: set xrange [xmin : xmax]
30: set yrange [0 : ymax]
31: set xlabel "x ->"
32: set ylabel "probability density ->"
33: set xtics autofreq
34: set ytics autofreq
35: set format x "%.1f"
36: set format y "%.1f"
37: set sample 200
38: set title "arcsin PDF with r = 2.0"
39: plot arcsin(x)
40: pause -1 "Hit return to continue"
41: set title "arcsin CDF with r = 2.0"
42: set yrange [0 : 1.1]
43: plot carcsin(x)
44: pause -1 "Hit return to continue"
45:
46: # Beta PDF and CDF
47: #p = 0.5; q = 0.7
48: #mu = p / (p + q)
49: #sigma = sqrt(p**q) / ((p + q ) * sqrt(p + q + 1.0))
50: #xmin = 0.0
51: #xmax = 1.0
52: #Mode of beta PDF used
53: #ymax = (p < 1.0 || q < 1.0) ? 2.0 : 1.1 * beta((p - 1.0)/(p + q - 2.0))
54: set key
55: set zeroaxis
56: #set xrange [xmin : xmax]
57: #set yrange [0 : ymax]
58: set xlabel "x ->"
59: set ylabel "probability density ->"
60: set xtics autofreq
61: set ytics autofreq
62: set format x "%.1f"
63: set format y "%.1f"
64: set sample 100
65: set title "beta PDF"
66: plot [0:1] [0:5] p = 0.5, q = 0.7, beta(x) title "p = 0.5, q = 0.7", \
67: p = 5.0, q = 3.0, beta(x) title "p = 5.0, q = 3.0", \
68: p = 0.5, q = 2.5, beta(x) title "p = 0.5, q = 2.5"
69: pause -1 "Hit return to continue"
70: set title "incomplete beta CDF"
71: plot [0:1] [0:1.1] p = 0.5, q = 0.7, cbeta(x) title "p = 0.5, q = 0.7", \
72: p = 5.0, q = 3.0, cbeta(x) title "p = 5.0, q = 3.0", \
73: p = 0.5, q = 2.5, cbeta(x) title "p = 0.5, q = 2.5"
74: pause -1 "Hit return to continue"
75:
76: # Binomial PDF and CDF
77: n = 25; p = 0.15
78: mu = n * p
79: sigma = sqrt(n * p * (1.0 - p))
80: xmin = int(mu - 4.0 * sigma)
81: xmin = xmin < 0 ? 0 : xmin
82: xmax = int(mu + 4.0 * sigma)
83: ymax = 1.1 * binom(mu) #Mode of normal PDF used
84: xinc = ceil((xmax - xmin) / 10)
85: xinc = xinc > 1 ? xinc : 1
86: set nokey
87: set nozeroaxis
88: set xrange [xmin : xmax]
89: set yrange [0 : ymax]
90: set xlabel "k ->"
91: set ylabel "probability density ->"
92: set xtics xmin + 0.499, xinc, xmax
93: set ytics 0, ymax / 10, ymax
94: set format x "%2.0f"
95: set format y "%3.2f"
96: set sample (xmax - xmin) + 1
97: set title "binomial PDF with n = 25, p = 0.15"
98: plot binom(x) with steps
99: pause -1 "Hit return to continue"
100: set title "binomial CDF with n = 25, p = 0.15"
101: set yrange [0 : 1.1]
102: set ytics 0, 1.1 / 10.5, 1.1
103: plot cbinom(x) with steps
104: pause -1 "Hit return to continue"
105:
106: # Cauchy PDF and CDF
107: #a = 0.0; b = 2.0
108: #cauchy PDF has no moments
109: #xmin = a - 4.0 * b
110: #xmax = a + 4.0 * b
111: #ymax = 1.1 * cauchy(a) #Mode of cauchy PDF used
112: set key
113: set zeroaxis
114: #set xrange [xmin : xmax]
115: #set yrange [0 : ymax]
116: set xlabel "x ->"
117: set ylabel "probability density ->"
118: set xtics autofreq
119: set ytics autofreq
120: set format x "%.1f"
121: set format y "%.2f"
122: set sample 100
123: set title "cauchy PDF"
124: plot [-15:15] [0:0.2] a = 0, b = 2, cauchy(x) title "a = 0, b = 2", \
125: a = 0, b = 4, cauchy(x) title "a = 0, b = 4"
126: pause -1 "Hit return to continue"
127: set title "cauchy CDF"
128: plot [-30:30] [0:1.1] a = 0, b = 2, ccauchy(x) title "a = 0, b = 2", \
129: a = 0, b = 4, ccauchy(x) title "a = 0, b = 4"
130: pause -1 "Hit return to continue"
131:
132: # Chi-square PDF and CDF
133: #df1 = 4.0
134: #mu = df1
135: #sigma = sqrt(2.0 * df1)
136: #xmin = mu - 4.0 * sigma
137: #xmin = xmin < 0 ? 0 : xmin
138: #xmax = mu + 4.0 * sigma
139: #ymax = 1.1 * (df1 > 2.0 ? chi(df1 - 2.0) : 1.0) #Mode of chi PDF used
140: set key
141: set zeroaxis
142: #set xrange [xmin : xmax]
143: #set yrange [0 : ymax]
144: set xlabel "x ->"
145: set ylabel "probability density ->"
146: set xtics autofreq
147: set ytics autofreq
148: set format x "%.1f"
149: set format y "%.2f"
150: set sample 100
151: set title "chi-square PDF"
152: plot [0:15] [0:0.2] df1 = 4, chi(x) title "df = 4", \
153: df1 = 6, chi(x) title "df = 6", \
154: df1 = 8, chi(x) title "df = 8"
155: pause -1 "Hit return to continue"
156: set title "chi-square CDF"
157: plot [0:15] [0:1.1] df1 = 4, cchi(x) title "df = 4", \
158: df1 = 6, cchi(x) title "df = 6", \
159: df1 = 8, cchi(x) title "df = 8"
160: pause -1 "Hit return to continue"
161:
162: # Erlang PDF and CDF
163: #lambda = 1.0; n = 2.0
164: #mu = n / lambda
165: #sigma = sqrt(n) / lambda
166: #xmin = mu - 4.0 * sigma
167: #xmin = xmin < 0 ? 0 : xmin
168: #xmax = mu + 4.0 * sigma
169: #ymax = n < 2.0 ? 1.0 : 1.1 * erlang((n - 1.0) / lambda) #Mode of erlang PDF used
170: set key
171: set zeroaxis
172: #set xrange [xmin : xmax]
173: #set yrange [0 : ymax]
174: set xlabel "x ->"
175: set ylabel "probability density ->"
176: set xtics autofreq
177: set ytics autofreq
178: set format x "%.1f"
179: set format y "%.1f"
180: set sample 100
181: set title "erlang PDF"
182: plot [0:10] [0:1] lambda = 1, n = 2, erlang(x) title "lambda = 1, n = 2", \
183: lambda = 2, n = 2, erlang(x) title "lambda = 2, n = 2"
184: pause -1 "Hit return to continue"
185: set title "erlang CDF"
186: plot [0:10] [0:1.1] lambda = 1, n = 2, cerlang(x) title "lambda = 1, n = 2", \
187: lambda = 2, n = 2, cerlang(x) title "lambda = 2, n = 2"
188: pause -1 "Hit return to continue"
189:
190: # Thanks to mrb2j@kelvin.seas.Virginia.EDU for telling us about this.
191: # Extreme (Gumbel extreme value) PDF and CDF
192: #alpha = 0.5; u = 1.0
193: #mu = u + (0.577215665/alpha) # Euler's constant
194: #sigma = pi/(sqrt(6.0)*alpha)
195: #xmin = mu - 4.0 * sigma
196: #xmax = mu + 4.0 * sigma
197: #ymax = 1.1 * extreme(u) #Mode of extreme PDF used
198: set key
199: set zeroaxis
200: #set xrange [xmin : xmax]
201: #set yrange [0 : ymax]
202: set xlabel "x ->"
203: set ylabel "probability density ->"
204: set xtics autofreq
205: set ytics autofreq
206: set format x "%.1f"
207: set format y "%.2f"
208: set sample 100
209: set title "extreme PDF"
210: plot [-10:10] [0:0.4] alpha = 0.5, u = 1.0, extreme(x) title "alpha = 0.5, u = 1.0", \
211: alpha = 1.0, u = 0.0, extreme(x) title "alpha = 1.0, u = 0.0"
212: pause -1 "Hit return to continue"
213: set title "extreme CDF"
214: plot [-10:10] [0:1.1] alpha = 0.5, u = 1.0, cextreme(x) title "alpha = 0.5, u = 1.0", \
215: alpha = 1.0, u = 0.0, cextreme(x) title "alpha = 1.0, u = 0.0"
216: pause -1 "Hit return to continue"
217:
218: # F PDF and CDF
219: #df1 = 5.0; df2 = 9.0
220: #mu = df2 < 2.0 ? 1.0 : df2 / (df2 - 2.0)
221: #sigma = df2 < 4.0 ? 1.0 : mu * sqrt(2.0 * (df1 + df2 - 2.0) / (df1 * (df2 - 4.0)))
222: #xmin = mu - 4.0 * sigma
223: #xmin = xmin < 0 ? 0 : xmin
224: #xmax = mu + 4.0 * sigma
225: #Mode of F PDF used
226: #ymax = df1 < 3.0 ? 1.0 : 1.1 * f((df1 / 2.0 - 1.0) / (df1 / 2.0 + df1 / df2))
227: set key
228: set zeroaxis
229: #set xrange [xmin : xmax]
230: #set yrange [0 : ymax]
231: set xlabel "x ->"
232: set ylabel "probability density ->"
233: set xtics autofreq
234: set ytics autofreq
235: set format x "%.1f"
236: set format y "%.2f"
237: set sample 100
238: set title "F PDF"
239: plot [0:4] [0:0.8] df1 = 5.0, df2 = 9.0, f(x) title "df1 = 5, df2 = 9", \
240: df1 = 7.0, df2 = 6.0, f(x) title "df1 = 7, df2 = 6"
241: pause -1 "Hit return to continue"
242: set title "F CDF"
243: plot [0:4] [0:1.1] df1 = 5.0, df2 = 9.0, cf(x) title "df1 = 5, df2 = 9", \
244: df1 = 7.0, df2 = 6.0, cf(x) title "df1 = 7, df2 = 6"
245: pause -1 "Hit return to continue"
246:
247: # Gamma PDF and incomplete gamma CDF
248: #rho = 0.5; lambda = 1.0
249: #mu = rho / lambda
250: #sigma = sqrt(rho) / lambda
251: #xmin = mu - 4.0 * sigma
252: #xmin = xmin < 0 ? 0 : xmin
253: #xmax = mu + 4.0 * sigma
254: #ymax = rho < 1.0 ? 2.0 : 1.1 * g((rho - 1.0) / lambda) #Mode of gamma pdf used
255: set key
256: set zeroaxis
257: #set xrange [xmin: xmax]
258: #set yrange [0: ymax]
259: set xlabel "x ->"
260: set ylabel "probability density ->"
261: set xtics autofreq
262: set ytics autofreq
263: set format x "%.1f"
264: set format y "%.1f"
265: set sample 100
266: set title "gamma PDF"
267: plot [0:5] [0:1.5] rho = 0.5, lambda = 1.0, g(x) title "rho = 0.5, lambda = 1.0", \
268: rho = 1.0, lambda = 1.0, g(x) title "rho = 1.0, lambda = 1.0", \
269: rho = 2.0, lambda = 2.0, g(x) title "rho = 2.0, lambda = 2.0"
270: pause -1 "Hit return to continue"
271: set title "incomplete gamma CDF (lambda == 1.0)"
272: plot [0:5] [0:1.1] rho = 0.5, cgamma(x) title "rho = 0.5", \
273: rho = 1.0, cgamma(x) title "rho = 1.0", \
274: rho = 2.0, cgamma(x) title "rho = 2.0"
275: pause -1 "Hit return to continue"
276:
277: # Geometric PDF and CDF
278: p = 0.4
279: mu = (1.0 - p) / p
280: sigma = sqrt(mu / p)
281: xmin = int(mu - 4.0 * sigma)
282: xmin = xmin < 0 ? 0 : xmin
283: xmax = int(mu + 4.0 * sigma)
284: xinc = ceil((xmax - xmin) / 10)
285: xinc = xinc > 1 ? xinc : 1
286: ymax = 1.1 * geometric(mu - 1/p) #mode of gamma PDF used
287: set nokey
288: set nozeroaxis
289: set xrange [xmin : xmax]
290: set yrange [0 : ymax]
291: set xlabel "k ->"
292: set ylabel "probability density ->"
293: set xtics xmin + 0.499, xinc, xmax
294: set ytics 0, ymax / 10, ymax
295: set format x "%2.0f"
296: set format y "%3.2f"
297: set sample (xmax - xmin) + 1
298: set title "geometric PDF with p = 0.4"
299: plot geometric(x) with steps
300: pause -1 "Hit return to continue"
301: set title "geometric CDF with p = 0.4"
302: set yrange [0 : 1.1]
303: set ytics 0, 1.1 / 10.5, 1.1
304: plot cgeometric(x) with steps
305: pause -1 "Hit return to continue"
306:
307: # Half normal PDF and CDF
308: mu = sqrt2invpi
309: sigma = 1.0
310: s = sigma*sqrt(1.0 - 2.0/pi)
311: xmin = 0.0
312: xmax = mu + 4.0 * s
313: ymax = 1.1 * halfnormal(0) #Mode of half normal PDF used
314: set nokey
315: set zeroaxis
316: set xrange [xmin: xmax]
317: set yrange [0: ymax]
318: set xlabel "x ->"
319: set ylabel "probability density ->"
320: set xtics autofreq
321: set ytics autofreq
322: set format x "%.1f"
323: set format y "%.1f"
324: set sample 100
325: set title "half normal PDF, sigma = 1.0"
326: plot halfnormal(x)
327: pause -1 "Hit return to continue"
328: set title "half normal CDF, sigma = 1.0"
329: set yrange [0:1.1]
330: plot chalfnormal(x)
331: pause -1 "Hit return to continue"
332:
333: # Hypergeometric PDF and CPF
334: nn = 75; mm = 25; n = 10
335: p = real(mm) / nn
336: mu = n * p
337: sigma = sqrt(real(nn - n) / (nn - 1.0) * n * p * (1.0 - p))
338: xmin = int(mu - 4.0 * sigma)
339: xmin = xmin < 0 ? 0 : xmin
340: xmax = int(mu + 4.0 * sigma)
341: xinc = ceil((xmax - xmin) / 10)
342: xinc = xinc > 1 ? xinc : 1
343: ymax = 1.1 * hypgeo(mu) #mode of binomial PDF used
344: set nokey
345: set nozeroaxis
346: set xrange [xmin : xmax]
347: set yrange [0 : ymax]
348: set xlabel "k ->"
349: set ylabel "probability density ->"
350: set xtics xmin + 0.499, xinc, xmax
351: set ytics 0, ymax / 10, ymax
352: set format x "%2.0f"
353: set format y "%3.2f"
354: set sample (xmax - xmin) + 1
355: set title "hypergeometric PDF with nn = 75, mm = 25, n = 10"
356: plot hypgeo(x) with steps
357: pause -1 "Hit return to continue"
358: set yrange [0 : 1.1]
359: set ytics 0, 1.1 / 10.5, 1.1
360: set title "hypergeometric CDF with nn = 75, mm = 25, n = 10"
361: plot chypgeo(x) with steps
362: pause -1 "Hit return to continue"
363:
364: # Laplace PDF
365: a = 0.0; b = 1.0
366: mu = a
367: sigma = sqrt(2.0) * b
368: xmin = mu - 4.0 * sigma
369: xmax = mu + 4.0 * sigma
370: ymax = 1.1 * laplace(a) #Mode of laplace PDF used
371: set nokey
372: set zeroaxis
373: set xrange [xmin: xmax]
374: set yrange [0: ymax]
375: set xlabel "x ->"
376: set ylabel "probability density ->"
377: set xtics autofreq
378: set ytics autofreq
379: set format x "%.1f"
380: set format y "%.2f"
381: set sample 100
382: set title "laplace (or double exponential) PDF with a = 0, b = 1"
383: plot laplace(x)
384: pause -1 "Hit return to continue"
385: set title "laplace (or double exponential) CDF with a = 0, b = 1"
386: set yrange [0: 1.1]
387: plot claplace(x)
388: pause -1 "Hit return to continue"
389:
390: # Logistic PDF and CDF
391: a = 0.0; lambda = 2.0
392: mu = a
393: sigma = pi / (sqrt(3.0) * lambda)
394: xmin = mu - 4.0 * sigma
395: xmax = mu + 4.0 * sigma
396: ymax = 1.1 * logistic(mu) #Mode of logistic PDF used
397: set nokey
398: set zeroaxis
399: set xrange [xmin: xmax]
400: set yrange [0: ymax]
401: set nokey
402: set zeroaxis
403: set xlabel "x ->"
404: set ylabel "probability density ->"
405: set xtics autofreq
406: set ytics autofreq
407: set format x "%.1f"
408: set format y "%.1f"
409: set sample 100
410: set title "logistic PDF with a = 0, lambda = 2"
411: plot logistic(x)
412: pause -1 "Hit return to continue"
413: set title "logistic CDF with a = 0, lambda = 2"
414: set yrange [0: 1.1]
415: plot clogistic(x)
416: pause -1 "Hit return to continue"
417:
418: # Lognormal PDF and CDF
419: mu = 1.0; sigma = 0.5
420: m = exp(mu + 0.5 * sigma**2)
421: s = sqrt(exp(2.0 * mu + sigma**2) * (2.0 * exp(sigma) - 1.0))
422: xmin = m - 4.0 * s
423: xmin = xmin < 0 ? 0 : xmin
424: xmax = m + 4.0 * s
425: ymax = 1.1 * lognormal(exp(mu - sigma**2)) #Mode of lognormal PDF used
426: set nokey
427: set zeroaxis
428: set xrange [xmin: xmax]
429: set yrange [0: ymax]
430: set xlabel "x ->"
431: set ylabel "probability density ->"
432: set xtics autofreq
433: set ytics autofreq
434: set format x "%.2f"
435: set format y "%.2f"
436: set sample 100
437: set title "lognormal PDF with mu = 1.0, sigma = 0.5"
438: plot lognormal(x)
439: pause -1 "Hit return to continue"
440: set title "lognormal CDF with mu = 1.0, sigma = 0.5"
441: set yrange [0: 1.1]
442: plot clognormal(x)
443: pause -1 "Hit return to continue"
444:
445: # Maxwell PDF
446: #a = 0.1
447: #mu = 2.0 / sqrt(pi) / a
448: #sigma = sqrt(3.0 - 8.0/pi) / a
449: #xmin = mu - 4.0 * sigma
450: #xmin = xmin < 0 ? 0 : xmin
451: #xmax = mu + 4.0 * sigma
452: #ymax = 1.1 * maxwell(1.0 / a) #Mode of maxwell PDF used
453: set key
454: set zeroaxis
455: #set xrange[xmin: xmax]
456: #set yrange[0: ymax]
457: set xlabel "x ->"
458: set ylabel "probability density ->"
459: set xtics autofreq
460: set ytics autofreq
461: set format x "%.1f"
462: set format y "%.1f"
463: set sample 100
464: set title "maxwell PDF"
465: plot [0:6] [0:1.4] a = 1.5, maxwell(x) title "a = 1.5", \
466: a = 1.0, maxwell(x) title "a = 1.0", \
467: a = 0.5, maxwell(x) title "a = 0.5"
468: pause -1 "Hit return to continue"
469: set title "maxwell CDF"
470: plot [0:6] [0:1.1] a = 1.5, cmaxwell(x) title "a = 1.5", \
471: a = 1.0, cmaxwell(x) title "a = 1.0", \
472: a = 0.5, cmaxwell(x) title "a = 0.5"
473: pause -1 "Hit return to continue"
474:
475: # Negative binomial PDF and CDF
476: r = 8; p = 0.4
477: mu = r * (1.0 - p) / p
478: sigma = sqrt(mu / p)
479: xmin = int(mu - 4.0 * sigma)
480: xmin = xmin < 0 ? 0 : xmin
481: xmax = int(mu + 4.0 * sigma)
482: xinc = ceil((xmax - xmin) / 10)
483: xinc = xinc > 1 ? xinc : 1
484: ymax = 1.1 * negbin(mu - 1.0/p) #mode of gamma PDF used
485: set nokey
486: set nozeroaxis
487: set xrange [xmin : xmax]
488: set yrange [0 : ymax]
489: set xlabel "k ->"
490: set ylabel "probability density ->"
491: set xtics xmin + 0.499, xinc, xmax
492: set ytics 0, ymax / 10, ymax
493: set format x "%2.0f"
494: set format y "%3.2f"
495: set sample (xmax - xmin) + 1
496: set title "negative binomial (or pascal or polya) PDF with r = 8, p = 0.4"
497: plot negbin(x) with steps
498: pause -1 "Hit return to continue"
499: set yrange [0 : 1.1]
500: set ytics 0, 1.1 / 10.5, 1.1
501: set title "negative binomial (or pascal or polya) CDF with r = 8, p = 0.4"
502: plot cnegbin(x) with steps
503: pause -1 "Hit return to continue"
504:
505: # Negative exponential PDF and CDF
506: lambda = 2.0
507: mu = 1.0 / lambda
508: sigma = 1.0 / lambda
509: xmax = mu + 4.0 * sigma
510: ymax = lambda #No mode
511: set nokey
512: set zeroaxis
513: set xrange [0: xmax]
514: set yrange [0: ymax]
515: set xlabel "x ->"
516: set ylabel "probability density ->"
517: set xtics autofreq
518: set ytics autofreq
519: set format x "%.2f"
520: set format y "%.1f"
521: set sample 100
522: set title "negative exponential (or exponential) PDF with lambda = 2.0"
523: plot nexp(x)
524: pause -1 "Hit return to continue"
525: set title "negative exponential (or exponential) CDF with lambda = 2.0"
526: set yrange [0: 1.1]
527: plot cnexp(x)
528: pause -1 "Hit return to continue"
529:
530: # Normal PDF and CDF
531: #mu = 0.0; sigma = 1.0
532: #xmin = mu - 4.0 * sigma
533: #xmax = mu + 4.0 * sigma
534: #ymax = 1.1 * normal(mu) #Mode of normal PDF used
535: set key
536: set zeroaxis
537: #set xrange [xmin: xmax]
538: #set yrange [0: ymax]
539: set xlabel "x ->"
540: set ylabel "probability density ->"
541: set xtics autofreq
542: set ytics autofreq
543: set format x "%.1f"
544: set format y "%.1f"
545: set sample 100
546: set title "normal (also called gauss or bell-curved) PDF"
547: plot [-4:4] [0:1] mu = 0, sigma = 1.0, normal(x) title "mu = 0, sigma = 1.0", \
548: mu = 2, sigma = 0.5, normal(x) title "mu = 2, sigma = 0.5", \
549: mu = 1, sigma = 2.0, normal(x) title "mu = 1, sigma = 2.0"
550: pause -1 "Hit return to continue"
551: set title "normal (also called gauss or bell-curved) CDF"
552: plot [-4:4] [0:1.1] mu = 0, sigma = 1.0, cnormal(x) title "mu = 0, sigma = 1.0", \
553: mu = 2, sigma = 0.5, cnormal(x) title "mu = 2, sigma = 0.5", \
554: mu = 1, sigma = 2.0, cnormal(x) title "mu = 1, sigma = 2.0"
555: pause -1 "Hit return to continue"
556:
557: # Pareto PDF and CDF
558: a = 1.0; b = 3.0
559: mu = a * b / (b - 1.0)
560: sigma = a * sqrt(b) / (sqrt(b - 2.0) * (b - 1.0))
561: xmin = mu - 4.0 * sigma
562: xmin = xmin < 0 ? 0 : xmin
563: xmax = mu + 4.0 * sigma
564: ymax = 1.1 * pareto(a) #mode of pareto PDF used
565: set nokey
566: set zeroaxis
567: set xrange [xmin: xmax]
568: set yrange [0: ymax]
569: set xlabel "x ->"
570: set ylabel "probability density ->"
571: set xtics autofreq
572: set ytics autofreq
573: set format x "%.1f"
574: set format y "%.1f"
575: set sample 500
576: set title "pareto PDF with a = 1, b = 3"
577: plot pareto(x)
578: pause -1 "Hit return to continue"
579: set title "pareto CDF with a = 1, b = 3"
580: set yrange [0: 1.1]
581: plot cpareto(x)
582: pause -1 "Hit return to continue"
583:
584: # Poisson PDF and CDF
585: mu = 4.0
586: sigma = sqrt(mu)
587: xmin = int(mu - 4.0 * sigma)
588: xmin = xmin < 0 ? 0 : xmin
589: xmax = int(mu + 4.0 * sigma)
590: xinc = ceil((xmax - xmin) / 10)
591: xinc = xinc > 1 ? xinc : 1
592: ymax = 1.1 * poisson(mu) #mode of poisson PDF used
593: set nokey
594: set nozeroaxis
595: set xrange [xmin : xmax]
596: set yrange [0 : ymax]
597: set xlabel "k ->"
598: set ylabel "probability density ->"
599: set xtics xmin + 0.499, xinc, xmax
600: set ytics 0, ymax / 10, ymax
601: set format x "%2.0f"
602: set format y "%3.2f"
603: set sample (xmax - xmin) + 1
604: set title "poisson PDF with mu = 4.0"
605: plot poisson(x) with steps
606: pause -1 "Hit return to continue"
607: set yrange [0 : 1.1]
608: set ytics 0, 1.1 / 10.5, 1.1
609: set title "poisson CDF with mu = 4.0"
610: plot cpoisson(x) with steps
611: pause -1 "Hit return to continue"
612:
613: # Rayleigh PDF and CDF
614: lambda = 2.0
615: mu = 0.5 * sqrt(pi / lambda)
616: sigma = sqrt((1.0 - pi / 4.0) / lambda)
617: xmax = mu + 4.0 * sigma
618: ymax = 1.1 * rayleigh(1.0 / sqrt(2.0 * lambda)) #Mode of rayleigh PDF used
619: set nokey
620: set zeroaxis
621: set xrange [0: xmax]
622: set yrange [0: ymax]
623: set xlabel "x ->"
624: set ylabel "probability density ->"
625: set xtics autofreq
626: set ytics autofreq
627: set format x "%.2f"
628: set format y "%.1f"
629: set sample 100
630: set title "rayleigh PDF with lambda = 2.0"
631: plot rayleigh(x)
632: pause -1 "Hit return to continue"
633: set title "rayleigh CDF with lambda = 2.0"
634: set yrange [0: 1.1]
635: plot crayleigh(x)
636: pause -1 "Hit return to continue"
637:
638: # Sine PDF and CDF
639: #a = 3.0; n = 2
640: #mu = a / 2.0
641: #sigma = sqrt(a * a / 3.0 * (1.0 - 3.0 / (2.0 * n * n * pi * pi)) - mu * mu)
642: #xmin = 0.0
643: #xmax = a
644: #ymax = 1.1 * 2.0 / a #Mode of sine PDF used
645: set key
646: set zeroaxis
647: #set xrange [xmin: xmax]
648: #set yrange [0: ymax]
649: set xlabel "x ->"
650: set ylabel "probability density ->"
651: set xtics autofreq
652: set ytics autofreq
653: set format x "%.2f"
654: set format y "%.1f"
655: set sample 100
656: set title "sine PDF"
657: plot [0:2] [0:1.1] a = 2.0, n = 1, sine(x) title "a = 2.0, n = 1", \
658: a = 2.0, n = 3, sine(x) title "a = 2.0, n = 3"
659: pause -1 "Hit return to continue"
660: set title "sine CDF"
661: plot [0:2] [0:1.1] a = 2.0, n = 1, csine(x) title "a = 2.0, n = 1", \
662: a = 2.0, n = 3, csine(x) title "a = 2.0, n = 3"
663: pause -1 "Hit return to continue"
664:
665: # t PDF and CDF
666: df1 = 3.0
667: mu = 0.0
668: sigma = df1 > 2.0 ? sqrt(df1 / (df1 - 2.0)) : 1.0
669: xmin = mu - 4.0 * sigma
670: xmax = mu + 4.0 * sigma
671: ymax = 1.1 * t(mu) #Mode of t PDF used
672: set nokey
673: set zeroaxis
674: set xrange [xmin: xmax]
675: set yrange [0: ymax]
676: set xlabel "x ->"
677: set ylabel "probability density ->"
678: set xtics autofreq
679: set ytics autofreq
680: set format x "%.1f"
681: set format y "%.2f"
682: set sample 100
683: set title "t PDF with df1 = 3.0"
684: plot t(x)
685: pause -1 "Hit return to continue"
686: set title "t CDF with df1 = 3.0"
687: set yrange [0: 1.1]
688: plot ct(x)
689: pause -1 "Hit return to continue"
690:
691: # Thanks to efrank@upenn5.hep.upenn.edu for telling us about this
692: # triangular PDF and CDF
693: m = 3.0
694: g = 2.0
695: mu = m
696: sigma = g/sqrt(6.0)
697: xmin = m - g
698: xmax = m + g
699: ymax = 1.1 * triangular(m) #Mode of triangular PDF used
700: set nokey
701: set zeroaxis
702: set xrange [xmin: xmax]
703: set yrange [0: ymax]
704: set xlabel "x ->"
705: set ylabel "probability density ->"
706: set xtics autofreq
707: set ytics autofreq
708: set format x "%.1f"
709: set format y "%.2f"
710: set sample 100
711: set title "triangular PDF with m = 3.0, g = 2.0"
712: plot triangular(x)
713: pause -1 "Hit return to continue"
714: set title "triangular CDF with m = 3.0, g = 2.0"
715: set yrange [0: 1.1]
716: plot ctriangular(x)
717: pause -1 "Hit return to continue"
718:
719: # Uniform PDF and CDF
720: a = -2.0; b= 2.0
721: mu = (a + b) / 2.0
722: sigma = (b - a) / sqrt(12.0)
723: xmin = a
724: xmax = b
725: ymax = 1.1 * uniform(mu) #No mode
726: set nokey
727: set zeroaxis
728: set xrange [xmin: xmax]
729: set yrange [0: ymax]
730: set xlabel "x ->"
731: set ylabel "probability density ->"
732: set xtics autofreq
733: set ytics autofreq
734: set format x "%.2f"
735: set format y "%.2f"
736: set sample 100
737: set title "uniform PDF with a = -2.0, b = 2.0"
738: plot uniform(x)
739: pause -1 "Hit return to continue"
740: set title "uniform CDF with a = -2.0, b = 2.0"
741: set yrange [0: 1.1]
742: plot cuniform(x)
743: pause -1 "Hit return to continue"
744:
745: # Weibull PDF and CDF
746: #lambda = 1.0; n = 1.5
747: #mu = lambda**(-1.0 / n) * gamma(1.0 / n) / n
748: #sigma = sqrt(2.0 * lambda**(-2.0 / n) * gamma(2.0 / n) / n - mu * mu)
749: #xmin = mu - 4.0 * sigma
750: #xmin = xmin < 0 ? 0 : xmin
751: #xmax = mu + 4.0 * sigma
752: #Mode of weibull PDF used
753: #ymax = 1.1 * (n > 1.0 ? weibull(((n - 1.0) / (lambda * n))**(1.0 / n)) : 2.0)
754: set key
755: set zeroaxis
756: #set xrange [xmin : xmax]
757: #set yrange [0: ymax]
758: set xlabel "x ->"
759: set ylabel "probability density ->"
760: set xtics autofreq
761: set ytics autofreq
762: set format x "%.2f"
763: set format y "%.1f"
764: set sample 100
765: set title "weibull PDF"
766: plot [0:2] [0:1.5] lambda = 1, n = 0.5, weibull(x) title "lambda = 1, n = 0.5", \
767: lambda = 1, n = 1.0, weibull(x) title "lambda = 1, n = 1.0", \
768: lambda = 1, n = 2.0, weibull(x) title "lambda = 1, n = 2.0", \
769: lambda = 3, n = 2.0, weibull(x) title "lambda = 3, n = 2.0"
770: pause -1 "Hit return to continue"
771: set title "weibull CDF"
772: plot [0:3] [0:1.2] lambda = 1, n = 0.5, cweibull(x) title "lambda = 1, n = 0.5", \
773: lambda = 1, n = 1.0, cweibull(x) title "lambda = 1, n = 1.0", \
774: lambda = 1, n = 2.0, cweibull(x) title "lambda = 1, n = 2.0", \
775: lambda = 3, n = 2.0, cweibull(x) title "lambda = 3, n = 2.0"
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