help mata mm_cauchy()
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Title

    mm_cauchy() -- Cauchy-Lorentz distribution


Syntax

        real matrix  mm_cauchyden(x, x0, gamma)

        real matrix  mm_cauchy(x, x0, gamma)

        real matrix  mm_cauchytail(x, x0, gamma)

        real matrix  mm_invcauchy(p, x0, gamma)


    where

            x:  real matrix x

            p:  real matrix p

           x0:  real scalar x0

        gamma:  real scalar gamma


Description

    mm_cauchyden() returns the density of the Cauchy-Lorentz distribution for
    the location parameter x0 and the scale parameter gamma.

    mm_cauchy() returns the cumulative distribution function of the
    Cauchy-Lorentz distribution for the location parameter x0 and the scale
    parameter gamma.

    mm_cauchytail() returns the right tail probability function of the
    Cauchy-Lorenz distribution for the location parameter x0 and the scale
    parameter gamma.

    mm_invcauchy() returns the inverse cumulative distribution function of
    the Cauchy-Lorentz distribution for the location parameter x0 and the
    scale parameter gamma.


Remarks

    cauchy(x,0,1) (the standard Cauchy distribution) is the Student t
    distribution with one degree of freedom.


Conformability

    mm_cauchyden(x, x0, gamma),
    mm_cauchy(x, x0, gamma),
    mm_cauchytail(x, x0, gamma):    
         x:  r x c
        x0:  1 x 1
     gamma:  1 x 1
    result:  r x c.

    mm_invcauchy(p, x0, gamma):
         p:  r x c
        x0:  1 x 1
     gamma:  1 x 1
    result:  r x c.


Diagnostics

    The functions return missing if gamma is not strictly positive.
    mm_invcauchy() returns missing if p is not in the unit interval.


Source code

    mm_cauchy.mata


References

    Programmed from http://en.wikipedia.org/wiki/Cauchy_distribution.


Author

    Christopher F Baum, Boston College


Also see