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# sympy.stats.Erlang

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

The density of the Erlang distribution is given by

.. math::
f(x) := \frac{\lambda^k x^{k-1} e^{-\lambda x}}{(k-1)!}

with :math:x \in [0,\infty].

Parameters(more...)


        def Erlang(name, k, l):
r"""
Create a continuous random variable with an Erlang distribution.

The density of the Erlang distribution is given by

.. math::
f(x) := \frac{\lambda^k x^{k-1} e^{-\lambda x}}{(k-1)!}

with :math:x \in [0,\infty].

Parameters
==========

k : Integer
l : Real number, \lambda > 0, the rate

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import Erlang, density, cdf, E, variance
>>> from sympy import Symbol, simplify, pprint

>>> k = Symbol("k", integer=True, positive=True)
>>> l = Symbol("l", positive=True)
>>> z = Symbol("z")

>>> X = Erlang("x", k, l)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
k  k - 1  -l*z
l *z     *e
---------------
gamma(k)

>>> C = cdf(X, meijerg=True)(z)
>>> pprint(C, use_unicode=False)
/  k*lowergamma(k, 0)   k*lowergamma(k, l*z)
|- ------------------ + --------------------  for z >= 0
<     gamma(k + 1)          gamma(k + 1)
|
\                     0                       otherwise

>>> simplify(E(X))
k/l

>>> simplify(variance(X))
k/l**2

References
==========

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



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_erlang():
k = Symbol("k", integer=True, positive=True)
l = Symbol("l", positive=True)

X = Erlang("x", k, l)