#| Pareto type III distribution in Racket/Gamble From Mathematica ParetoDistribution ParetoDistribution[k,1,gamma,mu] i.e. pareto_dist4(k,1,gamma,mu) This program was created by Hakan Kjellerstrand, hakank@gmail.com See also my Racket page: http://www.hakank.org/racket/ |# #lang gamble ; (require gamble/viz) (require racket) (require "gamble_utils.rkt") (require "gamble_distributions.rkt") #| variable : d 4.037469403703529: 1.0000000000019164e-5 2.8789990071647873: 1.0000000000019164e-5 9.624589269204671: 1.0000000000019164e-5 2.5212834981145793: 1.0000000000019164e-5 3.5147844751786996: 1.0000000000019164e-5 ... 2.5433163679454442: 1.0000000000019164e-5 5.017233307370223: 1.0000000000019164e-5 2.878124116842839: 1.0000000000019164e-5 2.8935488747781912: 1.0000000000019164e-5 3.884959744911844: 1.0000000000019164e-5 mean: 3.3353206853322455 HPD interval (0.84): 1.6387636600129816..4.466243135525829 HPD interval (0.9): 1.5235998608951222..5.022723368492755 HPD interval (0.99): 1.1811884763208926..8.979336548488584 HPD interval (0.99999): 1.032558216933082..57.79868963993348 Percentiles: (0.01 1.5053529146780749) (0.025 1.6679829245760724) (0.1 2.0361995671365642) (0.05 1.823699185768978) (0.25 2.4402986420754145) (0.5 3.001987721350424) (0.75 3.7762407592503626) (0.84 4.29751107352347) (0.9 4.867765614956472) (0.95 5.826401278468024) (0.975 7.014331219665171) (0.99 8.909648497091139) (0.999 16.4719391587291) Histogram: 1.033 : 1 # (1e-5 / 0 ) 1.636 : 2133 ####### (0.021 / 1e-5 ) 2.24 : 14766 ############################################# (0.147 / 0.021) 2.844 : 26468 ################################################################################ (0.264 / 0.169) 3.448 : 22925 ###################################################################### (0.229 / 0.433) 4.052 : 14045 ########################################### (0.140 / 0.662) 4.656 : 7835 ######################## (0.078 / 0.803) 5.26 : 4393 ############## (0.043 / 0.881) 5.864 : 2528 ######## (0.025 / 0.925) 6.468 : 1508 ##### (0.015 / 0.950) 7.072 : 975 ### (0.009 / 0.966) 7.675 : 641 ## (0.006 / 0.975) 8.279 : 441 ## (0.004 / 0.982) 8.883 : 331 ## (0.003 / 0.986) 9.487 : 226 # (0.002 / 0.989) 10.091: 172 # (0.001 / 0.992) 10.695: 131 # (0.001 / 0.993) 11.299: 83 # (0.000 / 0.995) 11.903: 56 # (0.000 / 0.996) 12.507: 73 # (0.000 / 0.996) 13.11 : 41 # (0.000 / 0.997) 13.714: 28 # (0.000 / 0.997) 14.318: 25 # (0.000 / 0.998) 14.922: 32 # (0.000 / 0.998) 15.526: 19 # (0.000 / 0.998) 16.13 : 17 # (0.000 / 0.998) 16.734: 13 # (0.000 / 0.998) 17.338: 14 # (0.000 / 0.999) 17.942: 7 # (7e-5 / 0.999) 18.546: 8 # (8e-5 / 0.999) 19.149: 5 # (5e-5 / 0.999) 19.753: 3 # (3e-5 / 0.999) 20.357: 2 # (2e-5 / 0.999) 20.961: 7 # (7e-5 / 0.999) 21.565: 3 # (3e-5 / 0.999) 22.169: 3 # (3e-5 / 0.999) 22.773: 3 # (3e-5 / 0.999) 23.377: 2 # (2e-5 / 0.999) 23.981: 3 # (3e-5 / 0.999) 24.584: 2 # (2e-5 / 0.999) 25.188: 3 # (3e-5 / 0.999) 25.792: 2 # (2e-5 / 0.999) 26.396: 2 # (2e-5 / 0.999) 27 : 2 # (2e-5 / 0.999) 27.604: 2 # (2e-5 / 0.999) 28.208: 0 (0 / 0.999) 28.812: 0 (0 / 0.999) 29.416: 1 # (1e-5 / 0.999) 30.02 : 0 (0 / 0.999) 30.623: 0 (0 / 0.999) 31.227: 1 # (1e-5 / 0.999) 31.831: 1 # (1e-5 / 0.999) 32.435: 0 (0 / 0.999) 33.039: 0 (0 / 0.999) 33.643: 0 (0 / 0.999) 34.247: 1 # (1e-5 / 0.999) 34.851: 2 # (2e-5 / 0.999) 35.455: 1 # (1e-5 / 0.999) 36.058: 1 # (1e-5 / 0.999) 36.662: 0 (0 / 0.999) 37.266: 1 # (1e-5 / 0.999) 37.87 : 1 # (1e-5 / 0.999) 38.474: 0 (0 / 0.999) 39.078: 0 (0 / 0.999) 39.682: 0 (0 / 0.999) 40.286: 0 (0 / 0.999) 40.89 : 0 (0 / 0.999) 41.494: 0 (0 / 0.999) 42.097: 1 # (1e-5 / 0.999) 42.701: 2 # (2e-5 / 0.999) 43.305: 2 # (2e-5 / 0.999) 43.909: 1 # (1e-5 / 0.999) 44.513: 0 (0 / 0.999) 45.117: 0 (0 / 0.999) 45.721: 0 (0 / 0.999) 46.325: 0 (0 / 0.999) 46.929: 0 (0 / 0.999) 47.532: 0 (0 / 0.999) 48.136: 0 (0 / 0.999) 48.74 : 1 # (1e-5 / 0.999) 49.344: 1 # (1e-5 / 0.999) 49.948: 0 (0 / 0.999) 50.552: 1 # (1e-5 / 0.999) 51.156: 0 (0 / 0.999) 51.76 : 0 (0 / 0.999) 52.364: 0 (0 / 0.999) 52.968: 0 (0 / 0.999) 53.571: 0 (0 / 0.999) 54.175: 0 (0 / 0.999) 54.779: 0 (0 / 0.999) 55.383: 0 (0 / 0.999) 55.987: 0 (0 / 0.999) 56.591: 0 (0 / 0.999) 57.195: 0 (0 / 0.999) variable : p #f: 0.9892200000038438 #t: 0.010780000000020648 mean: 0.010780000000020648 Histogram: #f: 99013 ################################################################################ (0.990 / 0 ) #t: 987 # (0.009 / 0.990) |# (define (model) (; enumerate ; rejection-sampler importance-sampler ; mh-sampler (define k 2) (define gamma 0.3) (define mu 1) (define d (pareto3_dist k gamma mu)) (define p (>= d (pareto3_quantile k gamma mu 0.99))) (list d p) ) ) (show-marginals (model) (list "d" "p" ) #:num-samples 100000 #:truncate-output 5 ; #:skip-marginals? #t ; #:show-stats? #t ; #:credible-interval 0.84 #:hpd-interval (list 0.84 0.9 0.99 0.99999) #:show-histogram? #t #:show-percentiles? #t ; #:burn 0 ; #:thin 0 )