/* 

  BUGS book, 2.3.1 in Picat.
  Page 17

  Cf my Gamble model gamble_bugs_book_2_3_1.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, ppl_common_utils.
import util.
% import ordset.

main => go.

/*

  var : x
  Probabilities (truncated):
  36.227393396346493: 0.0001000000000000
  29.634453123808932: 0.0001000000000000
  27.102741780728874: 0.0001000000000000
  26.830065960719224: 0.0001000000000000
  .........
  -9.598330602691806: 0.0001000000000000
  -10.071388204269972: 0.0001000000000000
  -11.000708729526696: 0.0001000000000000
  -18.34854276714066: 0.0001000000000000
  mean = 10.0167
  HPD intervals:
  HPD interval (0.84): 6.79470131294486..13.63299226564605


  theoretical_mean = 10

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           % show_simple_stats % ,
                           % show_percentiles,
                           show_hpd_intervals,hpd_intervals=[0.84]
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  println(theoretical_mean=student_t_dist_mean(10,2,4)),
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  % Note: The parameter order is different from Gamble's t-dist(4,10,2)
  X = student_t_dist(10,2,4), 
  
  add("x",X).