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The distribution of linear combinations of the sample occupancy numbers

1971; Elsevier BV; Volume: 74; Linguagem: Inglês

10.1016/s1385-7258(71)80019-7

1385-7258

Bernard Harris, C.J. Park,

Probability and Risk Models

Assume that a random sample of n observations has been taken from the multinomial distribution with N equiprobable cells. Let si, i = 0, 1, 2, …, n, be the number of cells occurring i times in the sample. Let W=∑i=0nwisi be a linear combination of the si's. In this paper we obtain a sufficient condition under which the asymptotic distribution of W is normal as n and N tend to infinity such that n/N → α>0.