We establish a large deviation approximation for the density function of an arbitrary sequence of random variables. The results are analogous to those obtained by Chaganty and Sethuraman (1985). We apply our theorems to the sample variance and the Mann–Whitney two-sample statistic.

It may not be an overstatement that one of the most widely reported measures of variation involves S <Superscript>2</Superscript>, the sample variance, which is also well-known to be alternatively expressed in the form of an U statistic with a symmetric kernel of degree 2 whatever be the population distribution function....</superscript>

We establish strong large deviation results for an arbitrary sequence of random variables under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic expansions for the tail probabilities of the same kind as those obtained by Bahadur and Rao (Ann....

A systematic method to deal with the interrelations of systems with multi-index quantities (random variables) is proposed. The method differs of the well-known Polykays. An application of the theoretical results here presented is the calculation of the moments of the sample variance for general...

The information contained in PP-plots is transformed into a single number. The resulting Harmonic Mass (HM) index is distribution free and its sample counterpart is shown to be consistent. For a wide class of CDFs the exact analytical expression of the distribution of the sample HM index is...