We derive exact distributions of weak record values in lattice as well as non-lattice cases. We obtain the Fisher information contained in the first m weak records and the first m (strong) records from a discrete distribution. We give geometric and Poisson examples.

Often, in industrial stress testing, meteorological data analysis, athletic events, and other similar situations, measurements may be made sequentially and only values larger or smaller than all previous ones are observed. When the number of records is fixed in advance, the data are referred to...

Suppose upper records were observed from a X-sequence of iid continuous random variables, and that another independent Y-sequence of iid variables from the same distribution is to be observed. In this paper, we then derive various exact distribution-free prediction intervals for records from the...

Let X1,n[less-than-or-equals, slant]X2,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n be the order statistics obtained from a sample from a continuous distribution and Zi,j,n=Xj,n/Xi,n be the ratio of order statistics. In this paper, asymptotic properties of Zi,j,n are...

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...