Inferences Based on Observed Frequencies
In this chapter we are concerned with the same type of problem as in the preceding chapter: the estimation of a parameter ϑ on the basis of observations. In the present chapter we shall restrict attention to observed frequencies h = x/n, where n denotes the number of trials and x the number of times a particular event has occurred. The frequency h is a random variable whose numerator x has a binomial distribution (§ 5). Other than on the known number n, the sample size, the binomial distribution depends only on a single parameter p, the probability of the event. In the case of several events with corresponding observed frequencies th i and probabilities p i , these p i may be either completely unknown or known functions of an unknown parameter ϑ. The problem is to estimate whatever is unknown and to study the reliability of the estimate.
KeywordsMaximum Likelihood Estimate Likelihood Function Asymptotic Distribution Unbiased Estimate Asymptotic Variance
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