/* 

  Cauchy dist (generating random samples)   in Picat.

  From Handbook on probability distributions
  page 86ff.

  See ppl_distributions.pi for the definitions of PDF, CDF, and quantile, and
  ppl_distributions_test.pi for tests of these.

  Cf my Gamble model gamble_cauchy-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 : g1
  Probabilities (truncated):
  20.446045442976306: 0.0001000000000000
  19.942374178810528: 0.0001000000000000
  17.923284197818901: 0.0001000000000000
  16.286526722561781: 0.0001000000000000
  .........
  0.0003532199238: 0.0001000000000000
  0.000349741314932: 0.0001000000000000
  0.000227678386393: 0.0001000000000000
  0.000094148929307: 0.0001000000000000
  mean = 2.00706

  var : g2
  Probabilities (truncated):
  23.339520321936742: 0.0001000000000000
  20.958626737041364: 0.0001000000000000
  17.608084603391141: 0.0001000000000000
  16.159683316342413: 0.0001000000000000
  .........
  0.000856518900832: 0.0001000000000000
  0.000181118569708: 0.0001000000000000
  0.000158708870351: 0.0001000000000000
  0.000079441829743: 0.0001000000000000
  mean = 2.02696

  var : mean (theoretical)
  Probabilities:
  2: 1.0000000000000000
  mean = 2.0


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
    
model() =>
  Delta = 1,
  Gamma = 2,
  G1 = gamma_dist(Delta,Gamma),
  G2 = gamma_dist(Delta,Gamma),

  Mean = gamma_dist_mean(Delta,Gamma),

  add("g1",G1),
  add("g2",G2),
  add("mean (theoretical)",Mean).