Abstract:
The paper considers the application of the Delaporte distribution to the analysis of the asymptotic behavior of the criterion capacities in the case of random samples in the task of testing a simple hypothesis concerning a one-dimensional parameter against a sequence of close alternatives. This distribution describes a random sample size.The concept of criterion power is introduced in this case. An asymptotic comparison of specific criteria (in the case of normal samples) is carried out using the concept of defect, which is an additional number of observations required by a competing criterion to asymptotically achieve the power of the best criterion.
Keywords:Delaporte distribution, power of test, level, asymptotic deficiency, hypotheses testing, efficiency, sample with random size, random index, asymptotic expansions, truncated Poisson distribution, truncated binomial distribution.
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