{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}