/* 

  Flights noshow in Picat.

  From "Resampling Stats Illustrations" (http://www.statistics101.net/PeterBruce_05-illus.pdf)
  Page 38
  """
  Hypothesis test for a difference in proportions
  (program “noshow”)
  Fly-By-Night Airways wishes to determine whether its business
  routes have a different passenger no-show rate than its vacation
  routes. It divides its routes into business and vacation, setting
  aside those routes that are neither. Taking a sample of 1000 reser-
  vations for each group, it determines that 384 passengers failed to
  show up on the business routes, while 341 failed to show up on the
  vacation routes. How likely is it that such a difference (43 or
  greater) occurred by chance, if the routes do not differ in this
  respect?
  ...
  If the two routes do not differ, then our best estimate of the overall
  no-show rate (our null hypothesis) is (384+341)/2000 = 36.3%. We
  now want to test whether 2 groups of 1000 drawn from this no-
  show rate are likely to show differences as great as those observed.
  -> 
  prob = .028
  """

  Cf my Gamble model gamble_flights_noshow.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 : business
  Probabilities (truncated):
  1004: 0.0310000000000000
  1000: 0.0290000000000000
  1001: 0.0280000000000000
  999: 0.0270000000000000
  .........
  959: 0.0010000000000000
  956: 0.0010000000000000
  952: 0.0010000000000000
  941: 0.0010000000000000
  mean = 999.86
  HPD intervals:
  HPD interval (0.94): 969.00000000000000..1030.00000000000000

  var : vacation
  Probabilities (truncated):
  1000: 0.0370000000000000
  1011: 0.0280000000000000
  1007: 0.0280000000000000
  997: 0.0270000000000000
  .........
  964: 0.0010000000000000
  961: 0.0010000000000000
  952: 0.0010000000000000
  949: 0.0010000000000000
  mean = 1000.56
  HPD intervals:
  HPD interval (0.94): 968.00000000000000..1028.00000000000000

  var : diff
  Probabilities (truncated):
  0: 0.0220000000000000
  -12: 0.0210000000000000
  -16: 0.0200000000000000
  3: 0.0190000000000000
  .........
  -56: 0.0010000000000000
  -58: 0.0010000000000000
  -73: 0.0010000000000000
  -79: 0.0010000000000000
  mean = -0.701
  HPD intervals:
  HPD interval (0.94): -43.00000000000000..40.00000000000000

  var : p
  Probabilities:
  false: 0.9710000000000000
  true: 0.0290000000000000
  mean = 0.029


*/
go ?=>
  reset_store,
  run_model(1000,$model,[show_probs_trunc,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() =>
  R = 0..1363,

  % Count how many of the 1000 bookings are within 0.999
  Business = [ V : V in resample(R), V < 1000].len,
  Vacation = [ V : V in resample(R), V < 1000].len,  


  Diff = Business - Vacation,
  P = check(Diff >= 43),

  add("business",Business),
  add("vacation",Vacation),
  add("diff",Diff),
  add("p",P).