Asymptotic equivalence of real probability distributions

ON CERTAm TYPES OF ASYMPTOTIC EQUIVALENCE OF REAL PROBABILITY DISTRIBUTIONS

Sadao Ikeda University of North Carolina Institute of Statistics~oSeries No. 455 Decemb.er,J..965 Con'tents Summary and 5.ntroduction 1. Definition of four types of asymptotic equivalence 2. Pr~erties of four types of asymptotic equivalence 3. Asymptotic independence of a set of random variables 4. Some classes of transformations of random variables pteserving the asymptotic equivalence in the ...

Possibility Equivalence of Unimodal Asymmetric Probability Distributions

− At the application level, it is important to be able to define around the measurement result an interval which will contain an important part of the distribution of the measured values, that is, a confidence interval. This practice acknowledged by the ISO Guide is a major shift from the probabilistic representation as a confidence interval represents a set of possible values for a parameter a...

Asymptotic probability distributions of some permutation statistics

We present in this work results on some distributions of permutation statistics of random elements of the wreath product Gr,n = Cr ! Sn. We consider the distribution of the descent number, the flag major index, the excedance, and the number of fixed points, over the whole group Gr,n or over the subclasses of derangements and involutions. We compute the mean, variance and moment generating funct...

Asymptotic estimates of elementary probability distributions

Several new asymptotic estimates (with precise error bounds) are derived for Poisson and binomial distributions as the parameters tend to infinity. The analytic methods used are also applicable to other discrete distribution functions. AMS 1991 Mathematical Subject Classification: 60A99 33B20.

I a - t ON CERTAIN TYPES OF ASYMPTOTIC EQUIVALENCE OF REAL PROBABILITY DISTRIBUTIONS II FURTHER RESULTS ON THE PROPERTIES OF TYPE