/* 

  CDF from data in Picat.

  cdf_from_data/1 is a simple way of creating a CDF from data.
  It uses get_probs/1 which gives the PDF.

  Here are also some related functions shown:
  - pdf_from_data/1
  - cdf_from_pdf/1,
  - quantile_from_cdf/2

  Note: Some of these are variants of existing functions, e.g.
  get_freqs/1, quantiles_data/2, etc.

  Cf my Gamble model gamble_cdf_from_data.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.

/*

  PDF:
  0 = 0.00008
  1 = 0.00029
  2 = 0.00211
  3 = 0.00758
  4 = 0.01885
  5 = 0.03772
  6 = 0.06375
  7 = 0.08827
  8 = 0.11246
  9 = 0.12427
  10 = 0.12452
  11 = 0.11497
  12 = 0.09638
  13 = 0.07371
  14 = 0.05269
  15 = 0.03411
  16 = 0.02123
  17 = 0.01248
  18 = 0.00724
  19 = 0.0038
  20 = 0.00193
  21 = 0.00078
  22 = 0.00044
  23 = 0.00018
  24 = 0.00008
  25 = 0.00003
  26 = 0.00003
  27 = 0.00002

  CDF:
  0 = 0.00008
  1 = 0.00037
  2 = 0.00248
  3 = 0.01006
  4 = 0.02891
  5 = 0.06663
  6 = 0.13038
  7 = 0.21865
  8 = 0.33111
  9 = 0.45538
  10 = 0.5799
  11 = 0.69487
  12 = 0.79125
  13 = 0.86496
  14 = 0.91765
  15 = 0.95176
  16 = 0.97299
  17 = 0.98547
  18 = 0.99271
  19 = 0.99651
  20 = 0.99844
  21 = 0.99922
  22 = 0.99966
  23 = 0.99984
  24 = 0.99992
  25 = 0.99995
  26 = 0.99998
  27 = 1.0

  Quantile:
  0.000001 = 0
  0.00001 = 0
  0.001 = 2
  0.01 = 3
  0.025 = 4
  0.05 = 5
  0.1 = 6
  0.25 = 8
  0.5 = 10
  0.75 = 12
  0.84 = 13
  0.9 = 14
  0.975 = 17
  0.99 = 18
  0.999 = 21
  0.99999 = 27
  0.999999 = 27

*/

go ?=>
  _ = random2(),
  % Data = binomial_dist_n(10,1/2,10000),
  Data = poisson_dist_n(10,100_000),
  % Data = [roundf(V,0.1) : V in normal_dist_n(100,15,100)],
  % Data = normal_dist_n(100,15,10000),
  
  
  PDF = pdf_from_data(Data),
  println("PDF:"),
  foreach(V=C in PDF)
    println(V=C)
  end,
  nl,

  % CDF = cdf_from_data(Data),
  CDF = cdf_from_pdf(PDF),
  
  println("CDF:"),
  foreach(V=C in CDF)
    println(V=C)
  end,
  nl,
  println("Quantile:"),
  foreach(Q in quantile_qs())
    println(Q=quantile_from_cdf(CDF,Q))
  end,
  nl.
go => true.