/* 

  Pareto type III distribution Picat.

  From Mathematica ParetoDistribution

  ParetoDistribution[k,1,gamma,mu]
  i.e. pareto_dist4(k,1,gamma,mu)


  Cf my Gamble model gamble_pareto3_dist.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*

  var : d
  Probabilities (truncated):
  54813.207905154296895: 0.0001000000000000
  22136.621979730352905: 0.0001000000000000
  19607.873809258242545: 0.0001000000000000
  17125.690850430641149: 0.0001000000000000
  .........
  0.300479905509335: 0.0001000000000000
  0.300373917676933: 0.0001000000000000
  0.300269754847247: 0.0001000000000000
  0.300114222060926: 0.0001000000000000
  mean = 28.0637
  [len = 10000,min = 0.300114,mean = 28.0637,median = 2.31472,max = 54813.2,variance = 458257.0,stdev = 676.947]

  var : p
  Probabilities:
  false: 0.8088000000000000
  true: 0.1912000000000000
  mean = 0.1912
  show_simple_stats: no numeric data


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           show_simple_stats % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  K = 2,
  Gamma = 0.3,
  Mu = 1,

  D = pareto3_dist(K,Gamma,Mu),
  P = check(D >= pareto3_dist_quantile(K,Gamma,Mu,0.99)),
  
  add("d",D),
  add("p",P).