In this note, we present some relationships between moments, central moments and cumulants from multivariate distributions. Recently, Smith (1995) presented four simple recursive formulas that translate moments to cumulants and vice versa. Here, we derive similar recursive formulas between the...

Suppose we know the combined number of upper and lower records and the current values of the lower and the upper records. Then, it is shown how various exact non-parametric confidence intervals can be constructed based on this information. Such intervals are exact and distribution-free in that...

The hazard function is an important characteristic for the analysis of reliability data. It is therefore of interest to see under what conditions it can be expressed as the product of a function of the variable and a function of the parameter. We show that such a factorization can be...

In this note a relation for product moments of order statistics is interpreted, extended, and applied to give a convenient formula for the variance of a lightly trimmed mean.

In this note, we present an alternate way of obtaining the sharp bound for expected values of order statistics derived by Moriguti (1953) based on the principle of greatest convex minorants. The formula presented here using an application of binomial--negative binomial relationship, in addition...

We consider an infinite sequence X1,X2,... of independent random variables having a common continuous distribution function F(x). For 1[less-than-or-equals, slant]i[less-than-or-equals, slant]n, let {Xi:n} denote the ith order statistic among X1,...,Xn. In this paper, we characterize the...

Starting from any univariate density function f(x) and an associated orthogonal function g(x), we present in this note a method of constructing multivariate distributions of all dimensions. It is shown that these multivariate distributions, in addition to being closed under marginal and...

In this paper, we consider the order statistics from a bivariate normal distribution and develop a conditional correlation analysis. We then apply these results to evaluate the presence of inventory effects in futures market. We also apply these results to analyze the data from a visual acuity...