/* 

  Pareto type IV distribution in Picat.

  From Mathematica ParetoDistribution.
  ParetoDistribution[k,alpha,gamma,mu]
  represents a Pareto type IV distribution with 
  - minimum parameter k, 
  - shape parameter alpha 
  - shape parameter gamma
  - location parameter mu

  Cf my Gamble model gamble_pareto4_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):
  194.575800643995763: 0.0001000000000000
  182.974310127591508: 0.0001000000000000
  151.803743450382996: 0.0001000000000000
  145.886281658358115: 0.0001000000000000
  .........
  1.000003477991948: 0.0001000000000000
  1.000002584333255: 0.0001000000000000
  1.000002463880333: 0.0001000000000000
  1.000002308074664: 0.0001000000000000
  mean = 2.20205
  [len = 10000,min = 1.0,mean = 2.20205,median = 1.26166,max = 194.576,variance = 25.0377,stdev = 5.00377]

  var : p
  Probabilities:
  false: 0.9769000000000000
  true: 0.0231000000000000
  mean = 0.0231
  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,
  Alpha = 3,
  Gamma = 1,
  Mu = 1.5,

  D = pareto4_dist(K,Alpha,Gamma,Mu),
  P = check(D >= pareto4_dist_quantile(K,Alpha,Gamma,Mu,0.99)),

  add("d",D),
  add("p",P).