How to resolve the algorithm Probabilistic choice step by step in the FutureBasic programming language

Published on 12 May 2024 09:40 PM
#Futurebasic

How to resolve the algorithm Probabilistic choice step by step in the FutureBasic programming language

Table of Contents

Problem Statement

Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values. The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Probabilistic choice step by step in the FutureBasic programming language

Source code in the futurebasic programming language

_elements = 8

local fn ProbabilisticChoice
  double prob(_elements), cumulative(_elements)
  Str15  item(_elements)
  double r, p, sum = 0, checksum = 0
  long   i, j, samples = 1000000
  
  item(1) = "aleph" : item(2) = "beth" : item(3) = "gimel" : item(4) = "daleth"
  item(5) = "he"    : item(6) = "waw"  : item(7) = "zayin" : item(8) = "heth"
  
  prob(1) = 1/5.0 : prob(2) = 1/6.0  : prob(3) = 1/7.0  : prob(4) = 1/8.0
  prob(5) = 1/9.0 : prob(6) = 1/10.0 : prob(7) = 1/11.0 : prob(8) = 1759/27720
  
  for i = 1 to _elements
    sum += prob(i)
  next
  if abs(sum-1) > samples then print "Probabilities don't sum to 1." : exit fn
  
  for i = 1 to samples
    cln r = (((double)arc4random()/0x100000000));
    p = 0
    for j = 1 to _elements
      p += prob(j)
      if (r < p) then cumulative(j) += 1 : exit for
    next
  next
  
  print
  printf @"Item      Actual    Theoretical"
  printf @"----      ------    -----------"
  for i = 1 to _elements
    printf @"%-7s %10.6f %12.6f", item(i), cumulative(i)/samples, prob(i)
    checksum += cumulative(i)/samples
  next
  printf @"         --------   -----------"
  printf @"%17.6f %12.6f", checksum, 1.000000
end fn

fn ProbabilisticChoice

HandleEvents

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