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# sympy.stats.UniformSum

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a continuous random variable with an Irwin-Hall distribution.

The probability distribution function depends on a single parameter
n which is an integer.

The density of the Irwin-Hall distribution is given by

.. math ::
f(x) := \frac{1}{(n-1)!}\sum_{k=0}^{\lfloor x\rfloor}(-1)^k
\binom{n}{k}(x-k)^{n-1}(more...)


        def UniformSum(name, n):
r"""
Create a continuous random variable with an Irwin-Hall distribution.

The probability distribution function depends on a single parameter
n which is an integer.

The density of the Irwin-Hall distribution is given by

.. math ::
f(x) := \frac{1}{(n-1)!}\sum_{k=0}^{\lfloor x\rfloor}(-1)^k
\binom{n}{k}(x-k)^{n-1}

Parameters
==========

n : A positive Integer, n > 0

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import UniformSum, density
>>> from sympy import Symbol, pprint

>>> n = Symbol("n", integer=True)
>>> z = Symbol("z")

>>> X = UniformSum("x", n)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
floor(z)
___
\
\         k         n - 1 /n\
)    (-1) *(-k + z)     *| |
/                         \k/
/__,
k = 0
--------------------------------
(n - 1)!

References
==========

.. [1] http://en.wikipedia.org/wiki/Uniform_sum_distribution
.. [2] http://mathworld.wolfram.com/UniformSumDistribution.html
"""

return rv(name, UniformSumDistribution, (n, ))


from sympy.stats import (P, E, where, density, variance, covariance, skewness,
given, pspace, cdf, ContinuousRV, sample,
Arcsin, Benini, Beta, BetaPrime, Cauchy,
Chi, ChiSquared,
ChiNoncentral, Dagum, Erlang, Exponential,

def test_uniformsum():
n = Symbol("n", integer=True)
_k = Symbol("k")

X = UniformSum('x', n)
`