# [R] using nls for gamma distribution (a,b,d)

Walmes Zeviani walmeszeviani at hotmail.com
Thu Apr 15 19:25:23 CEST 2010

```I never had seen someone using a density function for a mean function in
nonlinear regression. The convergence problem observed can be due the model
derivatives respect to the parameters. How could computationally be
d.gamma/d.alpha? digamma function? Does R understand this?

If your phenomena exhibit a gamma density form you could use a mean function
like:

fun <- function(x, alpha, beta, theta){
x*(alpha+beta*x)^(-1/theta)
}

da <- data.frame(x=1:20)
da\$y <- fun(da\$x, 1, 2, 0.9)+rnorm(da\$x,0,0.001)

plot(y~x, da)

n0 <- nls(y~fun(x, alpha, beta, theta), data=da,
start=list(alpha=1, beta=2, theta=0.9))

Or you can use a gamma density without the integration equal one. So, you
can replace the gamma(alpha) for B term:

gammafun <- function(x, alpha, B, b){
(1/B)*alpha^b*x^(b-1)*exp(-x/alpha)
}

curve(gammafun(x, 5, 1, 2), 0, 20)

da <- data.frame(x=1:20)
da\$z <- gammafun(da\$x, 5, 1, 2)+rnorm(da\$x,0,1)

plot(z~x, da)

n1 <- nls(z~gammafun(x, alpha, B, b), data=da,
start=list(alpha=5, B=1, b=2))

Sincerely.
Walmes.

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..ooo0
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..(....)... 0ooo...                              Walmes Zeviani
...\..(.....(.....)...     Master in Statistics and Agricultural
Experimentation
....\_)..... )../....       walmeszeviani at hotmail.com, Lavras - MG, Brasil
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