/* 

  Gumbel distribution in Picat.

  Picat> X=gumbel_dist_mean(0,1)
  X = -0.577215664901533

  Picat> X=gumbel_dist_mean(1/2,1)
  X = -0.077215664901533

  Picat> X=gumbel_dist_mean(1,2)
  X = -0.154431329803066

  Picat> X=gumbel_dist_mean(10,10)
  X = 4.227843350984672

  For more on this, see ppl_distributions.pi and ppl_distributions_test.pi

  Cf my Gamble model gamble_gumbel_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):
  2.363392278682258: 0.0001000000000000
  2.142426317642571: 0.0001000000000000
  2.133434736597891: 0.0001000000000000
  2.031851561502088: 0.0001000000000000
  .........
  -8.886411858714565: 0.0001000000000000
  -9.022808910850971: 0.0001000000000000
  -9.444955117185447: 0.0001000000000000
  -10.42135475152128: 0.0001000000000000
  mean = -0.577724
  HPD intervals:
  HPD interval (0.5): -0.81926243874067..0.62910448458625
  HPD interval (0.84): -1.98228612914739..1.24251922753499
  HPD interval (0.95): -3.08442918222517..1.65887736820801
  HPD interval (0.99): -4.94617907833505..1.88717577523671

  var : g2
  Probabilities (truncated):
  2.676857488673476: 0.0001000000000000
  2.639955412177302: 0.0001000000000000
  2.591816310820609: 0.0001000000000000
  2.564136140547906: 0.0001000000000000
  .........
  -7.417897745290895: 0.0001000000000000
  -7.487495408572753: 0.0001000000000000
  -7.667866125853207: 0.0001000000000000
  -8.231969377173893: 0.0001000000000000
  mean = -0.0708394
  HPD intervals:
  HPD interval (0.5): -0.26235153528547..1.20824559461863
  HPD interval (0.84): -1.56181175154084..1.65625466178057
  HPD interval (0.95): -2.63059880159420..2.08124847368757
  HPD interval (0.99): -4.28127199393900..2.40370933460692

  var : g3
  Probabilities (truncated):
  5.596881184575071: 0.0001000000000000
  5.335962630992857: 0.0001000000000000
  5.25999217543138: 0.0001000000000000
  5.066012772156643: 0.0001000000000000
  .........
  -14.725307938555575: 0.0001000000000000
  -17.739000273726479: 0.0001000000000000
  -18.467334516533395: 0.0001000000000000
  -22.658601617238528: 0.0001000000000000
  mean = -0.139515
  HPD intervals:
  HPD interval (0.5): -0.82124003789019..2.16157900376284
  HPD interval (0.84): -3.01237162578734..3.37418970415881
  HPD interval (0.95): -5.37961714452697..4.02742795455420
  HPD interval (0.99): -8.09404309249485..4.99889798119829

  var : g4
  Probabilities (truncated):
  32.268419100065657: 0.0001000000000000
  31.169944398525232: 0.0001000000000000
  30.716635753707962: 0.0001000000000000
  30.240839137315962: 0.0001000000000000
  .........
  -67.897309173807784: 0.0001000000000000
  -69.930330648007441: 0.0001000000000000
  -78.639745245167759: 0.0001000000000000
  -96.019747752920267: 0.0001000000000000
  mean = 4.38877
  HPD intervals:
  HPD interval (0.5): 2.38798408188151..17.16048430404739
  HPD interval (0.84): -9.59407478974397..22.09842896321442
  HPD interval (0.95): -21.46497724031714..25.10685117939627
  HPD interval (0.99): -36.99714985610558..27.56032801592956

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           show_hpd_intervals,hpd_intervals=[0.5,0.84,0.95,0.99]
                           ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  G1 = gumbel_dist(0,1),
  G2 = gumbel_dist(1/2,1),  
  G3 = gumbel_dist(1,2),
  G4 = gumbel_dist(10,10),

  add("g1",G1),
  add("g2",G2),
  add("g3",G3), 
  add("g4",G4).