A problem of minimax prediction for the multinomial and multivariate hypergeometric distribution is considered. A class of minimax predictors is determined for estimating linear combinations of the unknown parameter and the random variable having the multinomial or the multivariate hypergeometric distribution.
A class of minimax predictors of random variables with multinomial or multivariate hypergeometric distribution is determined in the case when the sample size is assumed to be a random variable with an unknown distribution. It is also proved that the usual predictors, which are minimax when the sample size is fixed, are not minimax, but they remain admissible when the sample size is an ancillary statistic with unknown distribution.
The problem of estimating the mean of a normal distribution is considered in the special case when the data arrive at random times. Certain classes of Bayes sequential estimation procedures are derived under LINEX and reflected normal loss function and with the observation cost determined by a function of the stopping time and the number of observations up to this time.
A Bayesian method of estimation of a success probability p is considered in the case when two experiments are available: individual Bernoulli (p) trials-the p-experiment-or products of r individual Bernoulli (p) trials-the -experiment. This problem has its roots in reliability, where one can test either single components or a system of r identical components. One of the problems considered is to find the degree r̃ of the -experiment and the size m̃ of the p-experiment such that the Bayes estimator...
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