src/probability/Distribution.py

   1 import random
   2
   3 class Distribution(object):
   4     """
   5     A general class representing a probability distribution.
   6     """
   7
   8     def __init__(self):
   9         """
  10         components is a list of probability distributions contained
  11         within this one. Right now, it's only used for sums of other
  12         distributions. This might change once I have a clearer idea of
  13         how it should work.
  14         """
  15         self.components = []
  16
  17
  18     def __add__(self, dist2):
  19         """
  20         Add another distribution to this one. Since we don't know what
  21         kind of distributions we'll be adding here, we return a new
  22         copy of the most general kind.
  23         """
  24         d = Distribution()
  25         d.components = self.components + dist2.components
  26         return d
  27
  28
  29     def sample(self):
  30         """
  31         Sample one value from the distribution.
  32         """
  33         if len(self.components) == 0:
  34             return None
  35         else:
  36             return sum([component.sample() for component in self.components])
  37
  38
  39     def cdf(self, x):
  40         """
  41         Evaluate the cumulative distribution function at x. Since we don't
  42         know our components, there is no good way to do this. Instead, we
  43         take a large number of samples, and see how many were less than or
  44         equal to x.
  45         """
  46         trials = 1000
  47         lte_count = 0
  48
  49         for i in range(0, trials):
  50             if self.sample() <= x:
  51                 lte_count += 1
  52
  53         return (float(lte_count) / float(trials))
  54
  55
  56
  57 class Uniform(Distribution):
  58     """
  59     Represents a uniform probability distribution.
  60     """
  61
  62     def __init__(self, a, b):
  63         """
  64         In subclasses, we know that there are no other components. For
  65         example, a uniform distribution is just made up of a uniform
  66         distribution and not, say, the sum of two uniforms (because
  67         that would no longer be uniform).
  68         """
  69         self.components = [self]
  70         self.min = float(min(a,b))
  71         self.max = float(max(a,b))
  72
  73
  74     def sample(self):
  75         return random.uniform(self.min, self.max)
  76
  77
  78     def cdf(self, x):
  79         """
  80         We can evaluate the CDF in special cases like this.
  81         """
  82         x = float(x)
  83
  84         if x <= self.min:
  85             return 0.0
  86         elif x >= self.max:
  87             return 1.0
  88         else:
  89             # x is somewhere between self.min and self.max and is equally
  90             # likely to be at all points in between; so, we just compute
  91             # "how far" through the interval (self.min, self.max) is as a
  92             # fraction of the whole, and return that.
  93             return ((x - self.min) / (self.max - self.min))