Determining the Size of a Finite Population of Different Objects from a Finite Sample taken at Random with Replacement

This paper gives a parsimonious solution to a standard variant of the classical Collector's Problem. A new computational formula based on a recursion is derived which extends the limits of tables and greatly speeds up their calculation.     

Large Deviations for Sums of Independent Non Identically Distributed Random Variables

This article considers large deviation results for sums of independent non identically distributed random variables, generalizing the result of Petrov (1968 Petrov , V. V. ( 1968 ). Asymptotic behavior of probabilities of large deviations . Theor. Probab. Appl. 13 : 408 – 420 . [Google Scholar]) by using a weaker and more natural condition on bounds of the cumulant generating functions of the sequence of random variables.     

On Large Deviations of Sums of Independent Random Variables

Extensions of some limit theorems are proved for tail probabilities of sums of independent identically distributed random variables satisfying the one-sided or two-sided Cramér's condition. The large deviation x-region under consideration is broader than in the classical Cramér's theorem, and the estimate of the remainder is uniform with respect to x. The corresponding asymptotic expansion with arbitrarily many summands is also obtained.     

Application of Concomitants of Order Statistics of Independent Non Identically Distributed Random Variables in Estimation

In this article, we obtain expressions for the pdf of a single concomitant of order statistic and the joint pdf of a pair of concomitants of order statistics of independent non identically distributed random variables. Using these expressions, we find the means, variances and covariances of order statistics arising from independent non identically distributed bivariate Pareto distributions. A method of estimation of a common parameter involved in several bivariate Pareto distributions using concomitants of order statistics is also discussed.     

The Joint Distribution of the Sum and the Maximum of IID Exponential Random Variables

The authors establish the joint distribution of the sum X and the maximum Y of IID exponential random variables. They derive exact formuli describing the random vector (X, Y), including its joint PDF, CDF, and other characteristics; marginal and conditional distributions; moments and related parameters; and stochastic representations leading to further properties of infinite divisibility and self-decomposability. The authors also discuss parameter estimation and include an example from climatology that illustrates the modeling potential of this new bivariate model.     

The Probability Distribution for the Number of Successes in Independent Trials

The number of successes S in n independent trials is one of the classic distributions in statistics. When the probability of success p is constant, S has the binomial distribution with parameters n and p. Distributional properties of S in the homogeneous case are well known, but they are considerably harder to establish when p varies. A brief historical review is undertaken to highlight some of the more important results obtained over the past 50 years. In spite of the progress made, there are still some important open problems concerning stochastic comparisons for S that deserve to be solved!