**From:** Spencer Graves (*spencer.graves@pdf.com*)

**Date:** Sun 16 May 2004 - 06:38:38 EST

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Message-id: <40A67FCE.6030807@pdf.com>

1. Have you considered parameterizing the problem in terms of

(Theta1, Theta2, Theta3), and then computing Theta4 <-

(1-Theta1-Theta2-Theta3) in the function you ask "optim" to optimize?

2. Beyond this, I don't understand what you are trying to do. Do

you want to estimate a multinomial approximation to a normal

distribution? If yes, are you given the mean and standard deviation of

the normal distribution PLUS the break points? If yes, then what about

the following:

* > Breaks <- 1:3
*

* > Mean <- 0
*

* > Sd <- 1
*

* > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
*

* > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
*

* > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
*

* > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
*

* > Breaks <- 1:3
*

* > Mean <- 0
*

* > Sd <- 1
*

* > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
*

* > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
*

* > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
*

* > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
*

* > Theta1;Theta2;Theta3;Theta4
*

[1] 0.8413447

[1] 0.1359051

[1] 0.862745

[1] 0.001349898

hope this helps. spencer graves

Dean Lee wrote:

*> Hi,
*

*> I am trying to do parameter estimation with optim, but I can't get it
*

*> to work quite right-- I have an equation X = Y where X is a gaussian,
*

*> Y is a multinomial distribution, and I am trying to estimate the
*

*> probabilities of Y( the mean and sd of X are known ), Theta1, Theta2,
*

*> Theta3, and Theta4; I do not know how I can specify the constraint
*

*> that Theta1 + Theta2 + Theta3 + Theta4 = 1 in optim. Is there another
*

*> method/package that I should use for this?
*

*> Also, I wonder if there's a more elegant way to code this equation in
*

*> R; right now my function looks something like Y/rnorm( 10000, mean,
*

*> sd), and I try to maximize it to 1; is it possible to "plug" the
*

*> entire gaussian( instead of using rnorm ) into the equation? Thanks.
*

*>
*

*> Regards,
*

*>
*

*> -Dean
*

*>
*

*> ______________________________________________
*

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*

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*

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*

*> http://www.R-project.org/posting-guide.html
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