/* 

  Pareto type II distribution in Picat.

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

  Cf my Gamble model gamble_pareto2_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):
  50.672960015629542: 0.0001000000000000
  46.089334508696915: 0.0001000000000000
  41.323229715073097: 0.0001000000000000
  37.660891819075538: 0.0001000000000000
  .........
  3.500219106244304: 0.0001000000000000
  3.50015276147717: 0.0001000000000000
  3.500109378724807: 0.0001000000000000
  3.500065889204516: 0.0001000000000000
  mean = 4.49397
  [len = 10000,min = 3.50007,mean = 4.49397,median = 4.02297,max = 50.673,variance = 3.03325,stdev = 1.74162]

  var : p
  Probabilities:
  false: 0.9808000000000000
  true: 0.0192000000000000
  mean = 0.0192
  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,
  Mu = 1.5,

  D = pareto2_dist(K,Alpha,Mu),
  P = check(D >= pareto2_dist_quantile(K,Alpha,Mu,0.99)),
  
  add("d",D),
  add("p",P).