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Create a continuous random variable with a Dagum distribution.

The density of the Dagum distribution is given by

.. math::
    f(x) := \frac{a p}{x} \left( \frac{\left(\tfrac{x}{b}\right)^{a p}}
            {\left(\left(\tfrac{x}{b}\right)^a + 1 \right)^{p+1}} \right)

with :math:`x > 0`.
(more...)

        def Dagum(name, p, a, b):
    r"""
    Create a continuous random variable with a Dagum distribution.

    The density of the Dagum distribution is given by

    .. math::
        f(x) := \frac{a p}{x} \left( \frac{\left(\tfrac{x}{b}\right)^{a p}}
                {\left(\left(\tfrac{x}{b}\right)^a + 1 \right)^{p+1}} \right)

    with :math:`x > 0`.

    Parameters
    ==========

    p : Real number, `p > 0`, a shape
    a : Real number, `a > 0`, a shape
    b : Real number, `b > 0`, a scale

    Returns
    =======

    A RandomSymbol.

    Examples
    ========

    >>> from sympy.stats import Dagum, density
    >>> from sympy import Symbol, simplify

    >>> p = Symbol("p", positive=True)
    >>> b = Symbol("b", positive=True)
    >>> a = Symbol("a", positive=True)
    >>> z = Symbol("z")

    >>> X = Dagum("x", p, a, b)

    >>> density(X)(z)
    a*p*(z/b)**(a*p)*((z/b)**a + 1)**(-p - 1)/z

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Dagum_distribution
    """

    return rv(name, DagumDistribution, (p, a, b))
        


src/s/y/sympy-HEAD/sympy/stats/tests/test_continuous_rv.py   sympy(Download)
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,
    a = Symbol("a", positive=True)
 
    X = Dagum('x', p, a, b)
    assert density(X)(x) == a*p*(x/b)**(a*p)*((x/b)**a + 1)**(-p - 1)/x