/* 

  Spread of traits in Picat.

  From http://godplaysdice.blogspot.com/2007/09/more-men-at-top-and-at-bottom.html
  """
  More men at the top, and at the bottom. 

  As has been documented by a lot of people, it seems that a lot of psychological traits 
  have the following properties:

  - men and women have approximately the same average for this trait, and
  - both genders have an approximately normal distribution for this trait, but
  - the distribution of men's values for this trait has a larger standard deviation 
    than the women's values
  """

  Cf my Gamble model gamble_spread_of_traits.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.

/*
  Here we model this by using a gaussian 100 with stdev=20 for men and stdev=10 for women.
  As can be seen, the range for men is much larger than for women. However, the probability
  that women has higher value than men is (still) 0.5.

  var : men
  mean = 99.911
  [min = 22.7614,mean = 99.911,median = 99.5458,max = 189.514,variance = 400.484,stdev = 20.0121]
  HPD intervals:
  HPD interval (0.84): 73.37903321225750..129.28031852979359
  HPD interval (0.9): 65.53899247688335..131.15500942530201
  HPD interval (0.95): 61.35180048170533..139.81534443592830
  HPD interval (0.99): 48.14623495277832..151.31420104059453

  var : women
  mean = 99.9721
  [min = 62.3324,mean = 99.9721,median = 100.013,max = 136.305,variance = 100.879,stdev = 10.0439]
  HPD intervals:
  HPD interval (0.84): 86.23514669347946..114.47483798265237
  HPD interval (0.9): 83.15737982376066..116.10328340263663
  HPD interval (0.95): 80.14976514768408..119.02297598964398
  HPD interval (0.99): 75.00086603533137..126.68575088480048

  var : diff
  mean = -0.0611296
  [min = -88.0243,mean = -0.0611296,median = -0.309563,max = 88.1071,variance = 500.976,stdev = 22.3825]
  HPD intervals:
  HPD interval (0.84): -28.91372015928050..34.08250317484425
  HPD interval (0.9): -36.69458083247871..36.36843108956859
  HPD interval (0.95): -44.77494369585491..42.63348950427753
  HPD interval (0.99): -57.03870327219290..58.88567951234310

  var : p
  mean = 0.505
  [min = 0,mean = 0.505,median = 1.0,max = 1,variance = 0.249975,stdev = 0.499975]
  HPD intervals:
  HPD interval (0.84): 0.00000000000000..1.00000000000000
  HPD interval (0.9): 0.00000000000000..1.00000000000000
  HPD interval (0.95): 0.00000000000000..1.00000000000000
  HPD interval (0.99): 0.00000000000000..1.00000000000000

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[mean,show_simple_stats,
                           % show_percentiles,
                           show_hpd_intervals,hpd_intervals=[0.84,0.9,0.95,0.99]
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Men = normal_dist(100,20),
  Women = normal_dist(100,10),

  Diff = Men - Women,
  P = check1(Women > Men),
  
  add("men",Men),
  add("women",Women),
  add("diff",Diff),
  add("p",P).