Search

Several approximations to the binomial distribution were compared in 1956 by Raft [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(l/n). In 1963, Bol'shev [2] gave two new Poisson-type approximations. In this paper, some of Raft's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values of p while the Camp-Paulson and Borges' approximations should generally be preferred for large p. [ABSTRACT FROM AUTHOR]

Let X[sub 1], ... X[sub r], be independent B(n,p) random variables. In this paper n is estimated with known p. The MLE is developed and shown to be consistent in a relative sense and asymptotically normal. Motivated by Y[sub i] = X[sub i]/q we consider Y[sub 1], ... ,Y[sub r] independent N(mu, mu) and examine three estimates of mu; (i) the MVUE, (ii) the MLE, and (iii) ?. These are shown to be asymptotically equivalent. [ABSTRACT FROM AUTHOR]