# Re: [R] MLE for two random variables

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Sun 13 Mar 2005 - 06:13:18 EST

Just to make sure, do you have any information on events when xu > u, i.e. do you know how many such events and you know u for those events? If yes, then that's called "censoring", not truncating. For that, the survival package seems pretty good. I found the information in Venables and Ripley, Modern Applied Statistics with S, helpful.

If you don't have data when xu > u, do you know u or must that be estimated also? In either case, I would likely use "optim", though "nlm" might work also. If I knew u and didn't have to estimate it, then I might combine the data as follows:

XU <- data.frame(x=c(x,xu),

u=c(rep(0, length(x)), rep(u, length(xu))))

If I needed to estimate u, I'd modify this as follows:

XU. <- data.frame(x=c(x,xu),

u=c(rep(0, length(x)), rep(1, length(xu))))

Then I'd write a function to compute, e.g, dev = (-2)*log(likelihood) and use optim or nlm to minimize this. If I had to estimate u, I might actually try to estimate ln.up = log(u-max(xu)); I may or may not get better numerical convergence using this than trying to estimate u directly.

```      hope this helps.
spencer graves

```

Carsten Steinhoff wrote:

>Hello,
>
>I've the following setting:
>
>(1) Data from a source without truncation (x)
>
>(2) Data from an other source with left-truncation at threshold u (xu)
>
>I have to fit a model on these these two sources, thereby I assume that both
>are "drawn" from the same distribution (eg lognormal). In a MLE I would sum
>the densities and maximize. The R-Function could be:
>
>function(x,xu,u,mu,sigma)
>dlnorm(x,mu,sigma)+(dlnorm(xu,mu,sigma)/(plnorm(u,mu,sigma)))
>
>So I tried to use the function FITDISTR for the MLE. But unfortunately it
>only accepts ONE random variable.
>Then I tried to combine x and xu in a vector, but that doesn't work, too,
>because the length of x and xu differs.
>
>Does anybody has a solution for my problem?
>
>
>Carsten
>
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