{smcl}
{* 15 March 2004}{...}
{hline}
help for {hi:nirand}  {right:Peter Lachenbruch program}
{hline}

{title:Generate random variables from N/I distributions}

{p 8 17 2}
{cmdab:nirand}
{it:newvar}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}] 
[{cmd:,}
[
{cmd:i} 
|
{cmdab:u:niform} 
|
{cmdab:v:mix}
|
{cmdab:n:ormal} 
| 
{cmdab:m:mix}
|
{cmd:c(}{it:#}{cmd:)} 
]
{cmd:m1(}{it:#}{cmd:)} 
{cmd:s1(}{it:#}{cmd:)}
{cmd:alpha(}{it:#}{cmd:)} 
{cmd:m2(}{it:#}{cmd:)}
{cmd:s2(}{it:#}{cmd:)}
]


{title:Description}

{p 4 4 2}{cmd:nirand} generates random variables from the normal/independent
family, usually ratios of a normal to an independent random variable.  The
numerator distribution will typically be a normal distribution with mean
{cmd:m1} (default 0) and standard deviation {cmd:s1} (default 1), but
optionally could be a mixture of two normals. The denominator may be specified
by an option: it defaults to {cmd:I}. 

{p 4 4 2}
{hi:You must set the number of observations before entering the program.}


{title:Options} 

{p 4 4 2}Only one of {cmd:i}, {cmd:uniform}, {cmd:vmix} {cmd:normal} {cmd:mmix} and {cmd:c()} may be
specified. 

{p 4 8 2}{cmd:i} specifies that the denominator distribution is a point mass of
1, leading to a normal random variable as output. This is the default, so 
the option is unnecessary. 

{p 4 8 2}{cmd:uniform} specifies that the denominator distribution is
uniform(0,1), leading to the slash distribution (with very long tails) as
output. 

{p 4 8 2} {cmd:vmix} specifies that the distribution is a {hi:mixture} of a normal distribution 
with mean m1 and standard deviation s1 and a {hi:slash} distribution with m2 and s2.

{p 4 8 2}{cmd:normal} specifies that the denominator is normal(0,1), leading
to a Cauchy distribution as output. 

{p 4 8 2} {cmd:mmix} specifies that the distribution is a {hi:mixture} of a normal distribution with mean m1 
and standard deviation s1 and a {hi:Cauchy} distribution with m2 and s2

{p 4 8 2} {cmd:c()} specifies that the denominator distribution is the square
root of a chi-square with {it:#} df leading to a (possibly non-central)
{it:t} distribution with {it:#} df as output. {it:#} need not be an integer. 

{p 4 8 2}{cmd:m1()} specifies the mean of the numerator distribution. The
default is 0. 

{p 4 8 2}{cmd:s1()} specifies the standard deviation of the numerator
distribution. The default is 1. 

{p 4 4 2}Note that the inverse of any of the denominator distributions may be
obtained by specifying {cmd:m1(1) s1(0)} and omitting {cmd:alpha()}, {cmd:m2()} 
and {cmd:s2()}.

{p 4 8 2}{cmd:alpha()} specifies that the numerator distribution will be an
{it:#} : (1 - {it:#}) mixture of two normal distributions. {it:#} must be
between 0 and 1.  The second component will be normal with mean given by
{cmd:m2()} and standard deviation given by {cmd:s2()}. Hence if {cmd:alpha()}
is specified, so too must be {cmd:m2()} and {cmd:s2()}. 
 
{p 4 8 2}{cmd:m2()} specifies the mean of the second component of the 
numerator distribution. See {cmd:alpha()} above. 

{p 4 8 2}{cmd:s2()} specifies the standard deviation of the second compoment 
of the numerator distribution. See {cmd:alpha()} above. 


{title:Examples} 

{p 4 8 2}A normal(10, 1):{p_end}
{p 4 8 2}{inp:. nirand normal, i m1(10) s1(1)} 

{p 4 8 2}A slash:{p_end}
{p 4 8 2}{inp:. nirand slash, uniform} 


{title:References}

{p 4 4 2}
Kafadar, K. 2003. John Tukey and robustness. {it:Statistical Science} 
18(3): 319-331. 

{p 4 4 2}
Hilbe, J. STB-28 sg44 for various random number generating programs

{title:Author}

{p 4 4 2}Peter A. Lachenbruch FDA/CBER/OBE{break} 
	 peter.lachenbruch@fda.hhs.gov