First see the distribution transformer data

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Nonparametric fit to grouped data with progressive censoring. For motivation, first see the distribution transformer data in Table 3.1 of Chapter 10. Suppose each of the K groups there is assumed here to have the same proportion T] failing in year 1, the same proportion πr2 failing in year 2, etc. The following method yields ML estimates of the proportions π~, π',. . . from the data on all groups.

(a) Write the separate multinomial log likelihoods for groups K through 1, denoting the number from group k failing in year m by yknl and the number surviving the last year by yI,L+I.

(b) From the total log likelihood calculate the likelihood equations.

(d) Derive formulas for all second partial derivatives of the total log

Table

Reference no: EM131056500

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