/* 

  pdf_all/cdf_all in Picat.

  Show all PDF, CDF given a distribution from some given quantiles.

  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.

main => go.

/*

dist = binomial_dist(10,1 / 6)
default quantiles: 0.01,0.99
PDF:
[q1 = 0,q2 = 5,diff = 5,prec = 1]
 0 0.161505582889846 
 1 0.323011165779692 
 2 0.290710049201722 
 3 0.155045359574252 
 4 0.054265875850988 
 5 0.013023810204237 
PDF:
[q1 = 0,q2 = 5,diff = 5,prec = 1]
 0 0.161505582889846 
 1 0.323011165779692 
 2 0.290710049201722 
 3 0.155045359574252 
 4 0.054265875850988 
 5 0.013023810204237 

quantiles 0.0001,0.9999
[q1 = 0,q2 = 6,diff = 6,prec = 1]
 0 0.161505582889846 
 1 0.323011165779692 
 2 0.290710049201722 
 3 0.155045359574252 
 4 0.054265875850988 
 5 0.013023810204237 
 6 0.00217063503404 
PDF:
[q1 = 0,q2 = 7,diff = 7,prec = 1]
 0 0.161505582889846 
 1 0.323011165779692 
 2 0.290710049201722 
 3 0.155045359574252 
 4 0.054265875850988 
 5 0.013023810204237 
 6 0.00217063503404 
 7 0.000248072575319 


dist = geometric(1 / 2)
default quantiles: 0.01,0.99
PDF:
[q1 = 0,q2 = 6,diff = 6,prec = 1]
 0 0.5 
 1 0.25 
 2 0.125 
 3 0.0625 
 4 0.03125 
 5 0.015625 
 6 0.0078125 
PDF:
[q1 = 0,q2 = 6,diff = 6,prec = 1]
 0 0.5 
 1 0.25 
 2 0.125 
 3 0.0625 
 4 0.03125 
 5 0.015625 
 6 0.0078125 

quantiles 0.0001,0.9999
[q1 = 0,q2 = 9,diff = 9,prec = 1]
 0 0.5 
 1 0.25 
 2 0.125 
 3 0.0625 
 4 0.03125 
 5 0.015625 
 6 0.0078125 
 7 0.00390625 
 8 0.001953125 
 9 0.0009765625 
PDF:
[q1 = 0,q2 = 13,diff = 13,prec = 1]
 0 0.5 
 1 0.25 
 2 0.125 
 3 0.0625 
 4 0.03125 
 5 0.015625 
 6 0.0078125 
 7 0.00390625 
 8 0.001953125 
 9 0.0009765625 
10 0.00048828125 
11 0.000244140625 
12 0.0001220703125 
13 0.00006103515625 


dist = poisson(1)
default quantiles: 0.01,0.99
PDF:
[q1 = 0,q2 = 4,diff = 4,prec = 1]
 0 0.367879441171443 
 1 0.367879441171442 
 2 0.183939720585721 
 3 0.06131324019524 
 4 0.01532831004881 
PDF:
[q1 = 0,q2 = 4,diff = 4,prec = 1]
 0 0.367879441171443 
 1 0.367879441171442 
 2 0.183939720585721 
 3 0.06131324019524 
 4 0.01532831004881 

quantiles 0.0001,0.9999
[q1 = 0,q2 = 5,diff = 5,prec = 1]
 0 0.367879441171443 
 1 0.367879441171442 
 2 0.183939720585721 
 3 0.06131324019524 
 4 0.01532831004881 
 5 0.003065662009762 
PDF:
[q1 = 0,q2 = 6,diff = 6,prec = 1]
 0 0.367879441171443 
 1 0.367879441171442 
 2 0.183939720585721 
 3 0.06131324019524 
 4 0.01532831004881 
 5 0.003065662009762 
 6 0.000510943668294 


pdf_all($normal(100,15),0.1,0.9
[q1 = 80.7767,q2 = 119.223,diff = 38.4465,prec = 1]
80.776726516830962 0.011699888795499 
81.776726516830962 0.012715146058557 
82.776726516830962 0.013757222931312 
83.776726516830962 0.014818696347 
84.776726516830962 0.015891285316878 
85.776726516830962 0.016965937146868 
86.776726516830962 0.018032937796952 
87.776726516830962 0.019082045093413 
88.776726516830962 0.020102642682592 
89.776726516830962 0.021083911814966 
90.776726516830962 0.022015017304534 
91.776726516830962 0.022885303354248 
92.776726516830962 0.023684494405498 
93.776726516830962 0.024402895786132 
94.776726516830962 0.025031588719771 
95.776726516830962 0.025562614235027 
96.776726516830962 0.025989140684458 
97.776726516830962 0.026305609949329 
98.776726516830962 0.026507857958002 
99.776726516830962 0.026593205865378 
100.776726516830962 0.02656051910246 
101.776726516830962 0.026410232476468 
102.776726516830962 0.026144340545228 
103.776726516830962 0.025766353563749 
104.776726516830962 0.025281220363135 
105.776726516830962 0.02469522053046 
106.776726516830962 0.024015829173142 
107.776726516830962 0.023251558338071 
108.776726516830962 0.022411779785066 
109.776726516830962 0.021506534265054 
110.776726516830962 0.020546332712197 
111.776726516830962 0.019541954821843 
112.776726516830962 0.018504250356696 
113.776726516830962 0.017443948214387 
114.776726516830962 0.016371477820371 
115.776726516830962 0.015296806806347 
116.776726516830962 0.014229298226514 
117.776726516830962 0.013177589784863 
118.776726516830962 0.012149496730749 

*/
go ?=>
  print_all($binomial_dist(10,1/6)),
  nl,
  print_all($geometric(1/2)),
  nl,
  print_all($poisson(1)),
  nl,
  println("pdf_all($normal(100,15),0.1,0.9"),
  pdf_all($normal(100,15),0.1,0.9).printf_list,
  nl,
  nl.
  
go => true.
  

print_all(Dist) =>
  println(dist=Dist),
  println("default quantiles: 0.01,0.99"),
  println("PDF:"),
  pdf_all(Dist).printf_list,
  println("PDF:"),
  pdf_all(Dist).printf_list,
  nl,
  println("quantiles 0.0001,0.9999"),
  pdf_all(Dist,0.0001,0.9990).printf_list,
  println("PDF:"),
  pdf_all(Dist,0.0001,0.9999).printf_list,
  nl.