```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

```