# Thread: maximum-likelihood estimators

1. ## maximum-likelihood estimators

Suppose that r-cylindrical shafts made by machine are selected at random from the production of the machine and their diameters and lengths measured. It is found R11 have both measurements with tolerance limits, R21 have satisfactory diameter but unsatisfactory lengths, and R22 are unsatisfactory as to both measurements.The total sum of Rij is r. Each shaft may be regarded as a drawing from multinomial population with density,
(p11)x11(p12)x12(p21)x21(1-p11-p12-p21)x22 for xij =0,1
having 3 parameters and the sum of all xij is 1. What are the maximum likelihood estimates of the parameters, R11=90, R12 =6,R21 =3, R22 =1?

how am i going to derive the mle for the parameters of multinomial distribution?

2. ## Re: maximum-likelihood estimators

Hey kimkimkibun.

You do it the same way you do for the Poisson distribution or any other distribution: start with your Likelihood function, differentiate with respect to the parameter you are estimating and find the maximum. The key thing is that you are finding the maximum and maximums are maximums whether they are discrete or continuous.