/* 

  Size of group of people in Picat.

  https://pedrozudo.github.io/docs/20_thesis/thesis_final_online_compressed.pdf
  page 86
  """
  Example 6.2. In this example we show how to model the size of a group of people
  as a Poisson distribution and answer queries about the size of the group using the
  comparison predicates > / 2 and =:= / 2 .
  1 n_people ~ poisson(6).
  2
  3 more_than_five:- n_people>5.
  4 exactly_five:- n_people=:=5.
  5
  6 query(more_than_five).
  7 query(exactly_five).
  """

  * > 5:
    Picat> X = 1 - poisson_dist_cdf(6,5)  
    X = 0.554320358635389

  * = 5:
    Picat> X = poisson_dist_pdf(6,5)    
    X = 0.16062314104798


  Cf my Gamble model gamble_size_of_group_of_people.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 : n people
  Probabilities:
  5: 0.1601000000000000
  6: 0.1509000000000000
  4: 0.1440000000000000
  7: 0.1348000000000000
  8: 0.1051000000000000
  3: 0.0919000000000000
  9: 0.0706000000000000
  2: 0.0418000000000000
  10: 0.0393000000000000
  11: 0.0235000000000000
  1: 0.0152000000000000
  12: 0.0102000000000000
  13: 0.0051000000000000
  0: 0.0035000000000000
  14: 0.0020000000000000
  15: 0.0014000000000000
  16: 0.0004000000000000
  17: 0.0002000000000000
  mean = 5.9752

  var : more than five
  Probabilities:
  true: 0.5435000000000000
  false: 0.4565000000000000
  mean = 0.5435

  var : exactly five
  Probabilities:
  false: 0.8399000000000000
  true: 0.1601000000000000
  mean = 0.1601

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  NPeople = poisson_dist(6),
  MoreThanFive = check(NPeople > 5),
  ExactlyFive = check(NPeople == 5),
  
  add("n people",NPeople),
  add("more than five",MoreThanFive),
  add("exactly five",ExactlyFive).