/

# Source code for sympy.stats.frv_types

"""
Finite Discrete Random Variables - Prebuilt variable types

Contains
========
FiniteRV
DiscreteUniform
Die
Bernoulli
Coin
Binomial
Hypergeometric
"""

from sympy.stats.frv import (SingleFinitePSpace, SingleFiniteDistribution)
from sympy import (S, sympify, Rational, binomial, cacheit, Symbol, Integer,
Dict, Basic)

__all__ = ['FiniteRV', 'DiscreteUniform', 'Die', 'Bernoulli', 'Coin',
'Binomial', 'Hypergeometric']

def rv(name, cls, *args):
density = cls(*args)
return SingleFinitePSpace(name, density).value

@property
def density(self):
return self.args[0]

def __new__(cls, density):
density = Dict(density)
return Basic.__new__(cls, density)

def FiniteRV(name, density):
"""
Create a Finite Random Variable given a dict representing the density.

Returns a RandomSymbol.

>>> from sympy.stats import FiniteRV, P, E

>>> density = {0: .1, 1: .2, 2: .3, 3: .4}
>>> X = FiniteRV('X', density)

>>> E(X)
2.00000000000000
>>> P(X>=2)
0.700000000000000
"""

class DiscreteUniformDistribution(SingleFiniteDistribution):
@property
def items(self):
return self.args

@property
def p(self):
return Rational(1, len(self.items))

@property
@cacheit
def density(self):
return dict((k, self.p) for k in self.set)

@property
def set(self):
return self.items

def pdf(self, x):
if x in self.items:
return self.p
else:
return S.Zero

def DiscreteUniform(name, items):
"""
Create a Finite Random Variable representing a uniform distribution over
the input set.

Returns a RandomSymbol.

Examples
========

>>> from sympy.stats import DiscreteUniform, density
>>> from sympy import symbols

>>> X = DiscreteUniform('X', symbols('a b c')) # equally likely over a, b, c
>>> density(X)
{a: 1/3, b: 1/3, c: 1/3}

>>> Y = DiscreteUniform('Y', range(5)) # distribution over a range
>>> density(Y)
{0: 1/5, 1: 1/5, 2: 1/5, 3: 1/5, 4: 1/5}

"""
return rv(name, DiscreteUniformDistribution, *items)

class DieDistribution(SingleFiniteDistribution):
_argnames = ('sides',)

@property
def set(self):
return map(Integer, range(1, self.sides+1))

def pdf(self, x):
x = sympify(x)
if x.is_Integer and x >= 1 and x <= self.sides:
return Rational(1, self.sides)
else:
return 0

def Die(name, sides=6):
"""
Create a Finite Random Variable representing a fair die.

Returns a RandomSymbol.

>>> from sympy.stats import Die, density

>>> D6 = Die('D6', 6) # Six sided Die
>>> density(D6)
{1: 1/6, 2: 1/6, 3: 1/6, 4: 1/6, 5: 1/6, 6: 1/6}

>>> D4 = Die('D4', 4) # Four sided Die
>>> density(D4)
{1: 1/4, 2: 1/4, 3: 1/4, 4: 1/4}
"""

return rv(name, DieDistribution, sides)

class BernoulliDistribution(SingleFiniteDistribution):
_argnames = ('p', 'succ', 'fail')

@property
@cacheit
def density(self):
return {self.succ: self.p, self.fail: 1 - self.p}

def Bernoulli(name, p, succ=1, fail=0):
"""
Create a Finite Random Variable representing a Bernoulli process.

Returns a RandomSymbol

>>> from sympy.stats import Bernoulli, density
>>> from sympy import S

>>> X = Bernoulli('X', S(3)/4) # 1-0 Bernoulli variable, probability = 3/4
>>> density(X)
{0: 1/4, 1: 3/4}

>>> X = Bernoulli('X', S.Half, 'Heads', 'Tails') # A fair coin toss
>>> density(X)
"""

return rv(name, BernoulliDistribution, p, succ, fail)

def Coin(name, p=S.Half):
"""
Create a Finite Random Variable representing a Coin toss.

Probability p is the chance of gettings "Heads." Half by default

Returns a RandomSymbol.

>>> from sympy.stats import Coin, density
>>> from sympy import Rational

>>> C = Coin('C') # A fair coin toss
>>> density(C)
{H: 1/2, T: 1/2}

>>> C2 = Coin('C2', Rational(3, 5)) # An unfair coin
>>> density(C2)
{H: 3/5, T: 2/5}
"""
return rv(name, BernoulliDistribution, p, 'H', 'T')

class BinomialDistribution(SingleFiniteDistribution):
_argnames = ('n', 'p', 'succ', 'fail')

@property
@cacheit
def density(self):
n, p, succ, fail = self.n, self.p, self.succ, self.fail
return dict((k*succ + (n - k)*fail,
binomial(n, k) * p**k * (1 - p)**(n - k)) for k in range(0, n + 1))

def Binomial(name, n, p, succ=1, fail=0):
"""
Create a Finite Random Variable representing a binomial distribution.

Returns a RandomSymbol.

Examples
========

>>> from sympy.stats import Binomial, density
>>> from sympy import S

>>> X = Binomial('X', 4, S.Half) # Four "coin flips"
>>> density(X)
{0: 1/16, 1: 1/4, 2: 3/8, 3: 1/4, 4: 1/16}
"""

return rv(name, BinomialDistribution, n, p, succ, fail)

class HypergeometricDistribution(SingleFiniteDistribution):
_argnames = ('N', 'm', 'n')

@property
@cacheit
def density(self):
N, m, n = self.N, self.m, self.n
N, m, n = map(sympify, (N, m, n))
density = dict((sympify(k),
Rational(binomial(m, k) * binomial(N - m, n - k),
binomial(N, n)))
for k in range(max(0, n + m - N), min(m, n) + 1))
return density

return dict((k, binomial(m, k) * binomial(N - m, n - k) / binomial(N, n))
for k in range(max(0, n + m - N), min(m, n) + 1))

def Hypergeometric(name, N, m, n):
"""
Create a Finite Random Variable representing a hypergeometric distribution.

Returns a RandomSymbol.

Examples
========

>>> from sympy.stats import Hypergeometric, density
>>> from sympy import S

>>> X = Hypergeometric('X', 10, 5, 3) # 10 marbles, 5 white (success), 3 draws
>>> density(X)
{0: 1/12, 1: 5/12, 2: 5/12, 3: 1/12}
"""
return rv(name, HypergeometricDistribution, N, m, n)