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{* 08 Jan 2004}{...}
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help for {hi:bnormpdf} {right: (version 1.1.0) }
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{title:Bivariate normal density function}

{p 7 16 2}{cmd:bnormpdf}
{it:x1_var x2_var}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}],
{cmdab:d:ensity:(}{it:newvar}{cmd:)}
[ {cmd:m1(}{it:#}{cmd:)}
{cmd:m2(}{it:#}{cmd:)}
{cmd:s1(}{it:#}{cmd:)}
{cmd:s2(}{it:#}{cmd:)}
{cmdab:r:ho(}{it:#}{cmd:)}
{cmdab:replace}
{cmdab:dou:ble} ]


{title:Description}

{p 4 4 2}
{cmd:bnormpdf} generates a new variable with the bivariate normal density for
the supplied variables {it:x1} and {it:x2}, with the joint distribution:

{p 8 8 2}({it:X1},{it:X2}) ~N( {cmd:m1}, {cmd:m2}, {cmd:s1}^2, {cmd:s2}^2, {cmd:rho})


{title:Options}

{p 4 8 2}{cmd:m1(}{it:#}{cmd:)} and {cmd:m2(}{it:#}{cmd:)} specify the expected values for {it:X1}
and {it:X2}.  The default for each is 0.

{p 4 8 2}{cmd:s1(}{it:#}{cmd:)} and {cmd:s2(}{it:#}{cmd:)}, the standard deviations for {it:X1} and {it:X2}, must be postive numbers.
The default for each is 1.

{p 4 8 2}{cmd:rho(}{it:#}{cmd:)}, the correlation, must be: {it:-1 < rho < 1}. The default is 0.

{p 4 8 2}{cmd:replace} allows an existing variable specified by {cmd:density()} to be overwritten.

{p 4 8 2}{cmd:double} specifies an 8 byte (double) storage type for the {cmd:density()} variable.
    The default storage type is float (4 byte).


{title:References}

{p 4 8 2} Bickel PH, Doksum KA. {it:Mathematical Statistics.} p.23-24.
Holden-Day.  Oakland. 1977.


{title:Examples}

{p 4 8}{inp:. bnormpdf x1 x2, dens(pdf_a) }

{p 4 8}{inp:. bnormpdf x1 x2, rho(.2) dens(pdf_b) double}

{p 4 8}{inp:. bnormpdf x1 x2, m1(.5) m2(1) s1(2) s2(1) rho(.2) dens(pdf_b) double replace}


{title:Author}

        Gary Longton, Fred Hutchinson Cancer Research Center, Seattle
        glongton@fhcrc.org


{title:Also see}

{p 0 9}On line: help for
{help probfun}