[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

Hi everybody,

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

This is my function to compute the first derivative:


    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

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Received on Wed Jul 05 01:25:57 2006

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