# [R] Problems when computing the 1rst derivative of mixtures of densities

From: Clément Viel <Clement.Viel_at_polytech-lille.net>
Date: Wed 05 Jul 2006 - 01:11:30 EST

I am currently working on mixtures of two densities ( f(xi,teta)= (1-teta)*f1(xi) + teta*f2(xi) ),
particularly on the behavior of the variance for teta=0 (so sample only comes from the first distribution).
To determine the maximum likelihood estimator I use the Newton-Rapdon Iteration. But when
computing the first derivative I get a none linear function (with several asymptotes) which is completely
absurd.

phy=function(teta,vect1,vect2){

return( sum(( vect2 - vect1) / (( 1 - teta) * vect1 + teta * vect2))) }

note: vect1 and vect2 contains values of the two distributions computed from sample previously extracted.

Beside, vect2 - vect1 is constant and ( 1 - teta) * vect1 + teta * vect2) is linear and always defined so I am expecting a linear function for the first derivative. To my mind, it's likely comes from the operation of division but I don't understand why results are skewed.

Have you got any suggestions, please?

```--
Clément Viel
Student in engineering school of Polytech-Lille
http://www.polytech-lille.fr

[[alternative HTML version deleted]]

______________________________________________
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help