#| Pareto type II distribution in Racket/Gamble From Mathematica ParetoDistribution ParetoDistribution[k,alpha,mu] represents a Pareto type II distribution with - minimum parameter k, - shape parameter alpha - location parameter 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 3.863769584762636: 1.0000000000019164e-5 2.9666233743467423: 1.0000000000019164e-5 1.5224498812465352: 1.0000000000019164e-5 1.904679572196017: 1.0000000000019164e-5 3.1198875237935955: 1.0000000000019164e-5 ... 2.6224883082446215: 1.0000000000019164e-5 1.760051383291585: 1.0000000000019164e-5 2.450167277752021: 1.0000000000019164e-5 1.8834125227989915: 1.0000000000019164e-5 1.5457955003278352: 1.0000000000019164e-5 mean: 2.4993382846040535 HPD interval (0.84): 1.500003964500889..3.202932266408794 HPD interval (0.9): 1.500003964500889..3.8226955652128014 HPD interval (0.99): 1.500003964500889..8.70373892027481 HPD interval (0.99999): 1.500003964500889..126.5102940639509 Percentiles: (0.01 1.5064101511339634) (0.025 1.5171496414619816) (0.1 1.5720266194684234) (0.05 1.5346310765879316) (0.25 1.7010462334987566) (0.5 2.0211280045679407) (0.75 2.691177496585534) (0.84 3.2029213465081474) (0.9 3.8226763088562015) (0.95 4.947647679068712) (0.975 6.361440416934013) (0.99 8.697086094219586) (0.999 19.60703320110644) Histogram: 1.5 : 1 # (1e-5 / 0 ) 2.83 : 77952 ################################################################################ (0.779 / 1e-5 ) 4.16 : 14100 ############### (0.141 / 0.779) 5.49 : 4154 ##### (0.041 / 0.920) 6.82 : 1734 ## (0.017 / 0.962) 8.149 : 837 # (0.008 / 0.979) 9.479 : 430 # (0.004 / 0.987) 10.809 : 233 # (0.002 / 0.992) 12.139 : 167 # (0.001 / 0.994) 13.469 : 83 # (0.000 / 0.996) 14.799 : 83 # (0.000 / 0.996) 16.129 : 40 # (0.000 / 0.997) 17.459 : 42 # (0.000 / 0.998) 18.789 : 29 # (0.000 / 0.998) 20.119 : 19 # (0.000 / 0.998) 21.448 : 11 # (0.000 / 0.999) 22.778 : 11 # (0.000 / 0.999) 24.108 : 12 # (0.000 / 0.999) 25.438 : 9 # (9e-5 / 0.999) 26.768 : 8 # (8e-5 / 0.999) 28.098 : 8 # (8e-5 / 0.999) 29.428 : 9 # (9e-5 / 0.999) 30.758 : 4 # (4e-5 / 0.999) 32.088 : 2 # (2e-5 / 0.999) 33.418 : 2 # (2e-5 / 0.999) 34.747 : 4 # (4e-5 / 0.999) 36.077 : 1 # (1e-5 / 0.999) 37.407 : 1 # (1e-5 / 0.999) 38.737 : 1 # (1e-5 / 0.999) 40.067 : 1 # (1e-5 / 0.999) 41.397 : 0 (0 / 0.999) 42.727 : 0 (0 / 0.999) 44.057 : 4 # (4e-5 / 0.999) 45.387 : 0 (0 / 0.999) 46.716 : 0 (0 / 0.999) 48.046 : 0 (0 / 0.999) 49.376 : 0 (0 / 0.999) 50.706 : 0 (0 / 0.999) 52.036 : 0 (0 / 0.999) 53.366 : 1 # (1e-5 / 0.999) 54.696 : 0 (0 / 0.999) 56.026 : 0 (0 / 0.999) 57.356 : 2 # (2e-5 / 0.999) 58.686 : 1 # (1e-5 / 0.999) 60.015 : 0 (0 / 0.999) 61.345 : 0 (0 / 0.999) 62.675 : 0 (0 / 0.999) 64.005 : 0 (0 / 0.999) 65.335 : 0 (0 / 0.999) 66.665 : 0 (0 / 0.999) 67.995 : 0 (0 / 0.999) 69.325 : 0 (0 / 0.999) 70.655 : 0 (0 / 0.999) 71.985 : 0 (0 / 0.999) 73.314 : 0 (0 / 0.999) 74.644 : 0 (0 / 0.999) 75.974 : 0 (0 / 0.999) 77.304 : 1 # (1e-5 / 0.999) 78.634 : 0 (0 / 0.999) 79.964 : 0 (0 / 0.999) 81.294 : 0 (0 / 0.999) 82.624 : 0 (0 / 0.999) 83.954 : 0 (0 / 0.999) 85.283 : 0 (0 / 0.999) 86.613 : 0 (0 / 0.999) 87.943 : 0 (0 / 0.999) 89.273 : 1 # (1e-5 / 0.999) 90.603 : 1 # (1e-5 / 0.999) 91.933 : 0 (0 / 0.999) 93.263 : 0 (0 / 0.999) 94.593 : 0 (0 / 0.999) 95.923 : 0 (0 / 0.999) 97.253 : 0 (0 / 0.999) 98.582 : 0 (0 / 0.999) 99.912 : 0 (0 / 0.999) 101.242: 0 (0 / 0.999) 102.572: 0 (0 / 0.999) 103.902: 0 (0 / 0.999) 105.232: 0 (0 / 0.999) 106.562: 0 (0 / 0.999) 107.892: 0 (0 / 0.999) 109.222: 0 (0 / 0.999) 110.552: 0 (0 / 0.999) 111.881: 0 (0 / 0.999) 113.211: 0 (0 / 0.999) 114.541: 0 (0 / 0.999) 115.871: 0 (0 / 0.999) 117.201: 0 (0 / 0.999) 118.531: 0 (0 / 0.999) 119.861: 0 (0 / 0.999) 121.191: 0 (0 / 0.999) 122.521: 0 (0 / 0.999) 123.851: 0 (0 / 0.999) 125.18 : 0 (0 / 0.999) variable : p #f: 0.9903100000038509 #t: 0.009690000000018613 mean: 0.009690000000018613 Histogram: #f: 99015 ################################################################################ (0.990 / 0 ) #t: 985 # (0.009 / 0.990) |# (define (model) (; enumerate ; rejection-sampler importance-sampler ; mh-sampler (define k 2) (define alpha 3) (define mu 1.5) (define d (pareto2_dist k alpha mu)) (define p (>= d (pareto2_quantile k alpha 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 0.90 0.99 0.99999) #:show-histogram? #t #:show-percentiles? #t ; #:burn 0 ; #:thin 0 )