SOME TOPICS RELATED TO TRANSFORMATIONS, DISTRIBUTION FUNCTIONS AND STOCHASTIC PROCESSES
STATE UNIV OF NEW YORK AT BUFFALO AMHERST
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This report is divided into four independent sections. Section 1 contains a theorem giving sufficient conditions for the asymptotic distribution of a standardized location-scale random variable to have the distribution of a power of the random variable, and examples showing that the conditions are not necessary. Section 2 gives illustrations of the problem of deciding whether or not one random variable is a transform of another and, in each case in which a transformation of the one random variable into the other is assured, the set of all such transformations is investigated. Section 3 consists of an example of the notion of robustness of a test as well as a tentative general definition of the concept of robustness of a test, and a brief study of the Kolmogorov metric on the space of location-parameter distributions. Section 4 presents simple iterative solutions of special systems of differential-difference equations, in which the constant coefficient matrices are triangular and satisfy conditions sufficient to insure that the solutions involve only exponential terms or terms that are products of linear factors and exponential factors. These methods are applied to the simple stochastic epidemic and to the general stochastic epidemic.
- Statistics and Probability