{smcl}
{* 09aug2007}{...}
{cmd:help mata mm_cauchy()}
{hline}

{title:Title}

{pstd}
    {bf:mm_cauchy() -- Cauchy-Lorentz distribution}


{title:Syntax}

{p 8 27 2}
    {it:real matrix}{space 1}
    {cmd:mm_cauchyden(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}

{p 8 27 2}
    {it:real matrix}{space 1}
    {cmd:mm_cauchy(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}

{p 8 27 2}
    {it:real matrix}{space 1}
    {cmd:mm_cauchytail(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}

{p 8 27 2}
    {it:real matrix}{space 1}
    {cmd:mm_invcauchy(}{it:p}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}


{pstd}
where

{p 12 16 2}
{it:x}:  {it:real matrix x} 

{p 12 16 2}
{it:p}:  {it:real matrix p} 

{p 11 16 2}
{it:x0}:  {it:real scalar x0}

{p 8 16 2}
{it:gamma}:  {it:real scalar gamma}


{title:Description}

{pstd}
    {cmd:mm_cauchyden()} returns the density of the Cauchy-Lorentz distribution for the
    location parameter {it:x0} and the scale parameter {it:gamma}.

{pstd}
    {cmd:mm_cauchy()} returns the cumulative distribution function of the Cauchy-Lorentz distribution for the
    location parameter {it:x0} and the scale parameter {it:gamma}.

{pstd}
    {cmd:mm_cauchytail()} returns the right tail probability function of the Cauchy-Lorenz distribution for the
    location parameter {it:x0} and the scale parameter {it:gamma}.
    
{pstd}
    {cmd:mm_invcauchy()} returns the inverse cumulative distribution function of the Cauchy-Lorentz distribution for the
    location parameter {it:x0} and the scale parameter {it:gamma}.
    

{title:Remarks}

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


{title:Conformability}

    {cmd:mm_cauchyden(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)},
    {cmd:mm_cauchy(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)},
    {cmd:mm_cauchytail(}{it:x}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}:    
         {it:x}:  {it:r x c}
        {it:x0}:  1 {it:x} 1
     {it:gamma}:  1 {it:x} 1
    {it:result}:  {it:r x c}.

    {cmd:mm_invcauchy(}{it:p}{cmd:,} {it:x0}{cmd:,} {it:gamma}{cmd:)}:
         {it:p}:  {it:r x c}
        {it:x0}:  1 {it:x} 1
     {it:gamma}:  1 {it:x} 1
    {it:result}:  {it:r x c}.


{title:Diagnostics}

{pstd}
    The functions return missing if {it:gamma} is not strictly 
    positive. {cmd:mm_invcauchy()} returns missing if {it:p} is not 
    in the unit interval.
    

{title:Source code}

{pstd}
    {help moremata_source##mm_cauchy:mm_cauchy.mata}


{title:References}

{phang}
    Programmed from {browse "http://en.wikipedia.org/wiki/Cauchy_distribution"}.


{title:Author}

{pstd}
    Christopher F Baum, Boston College


{title:Also see}

{psee}
    Online:  help for {helpb moremata}