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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