BACKGROUND It is usually preferable to model and estimate prevalence ratios instead of odds ratios in cross-sectional studies when diseases or injuries are not rare. Problems with existing methods of modeling prevalence ratios include lack of convergence, overestimated standard errors, and extrapolation of simple univariate formulas to multivariable models. We compare two of the newer methods u...

We prove the central limit theorem for the volume and the f -vector of the random polytope Pn and the Poisson random polytope Πn in a fixed convex polytope P ⊂ IR. Here Pn is the convex hull of n random points in P , and Πn is the convex hull of the intersection of a Poisson process X(n), of intensity n, with P . A general lower bound on the variance is also proved. ∗Supported by Hungarian Nati...

Let Kn be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on Rd. We establish variance asymptotics for the re-scaled volume and k-face functional of Kn, k ∈ {0, 1, ..., d − 1}, resolving an open problem. Asymptotic variances and the scaling limit of the boundary of Kn are given in terms of functionals of germ-grain models having parabolic gra...

We derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods. These methods are based on estimating functions motivated by a working "mixed-Poisson" assumption under which conditioning can eliminate subject-specific random effects. Robust pseudoscore test statistics are obtained via "sandwich" variance estim...

Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of earthquakes. We show that this process strongly departs from a Poisson statistics for both catalogue and sequence data sets. This indicate t...

This paper establishes expectation and variance asymptotics for statistics of the Poisson-Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surface area, Hausdorff measure, and the number of faces of lower-dimensional skeletons. We also consider the complexity of the so-called Voronoi zone an...

Abstract The Poisson-Modification of Quasi Lindley (PMQL) distribution is a newly introduced mixed Poisson for over-dispersed count data. aim this article to introduce the Zero-modified PMQL (ZMPMQL) as an alternative in order accommodate zero inflation/deflation. method obtaining ZMPMQL jointly with some its important properties, namely probability mass and functions, mean, variance, index dis...

Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We...

In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its v...

Abstract Al-Osh and Alzaid (1988) consider a Poisson moving average (PMA) model to describe the relation among integer-valued time series data; this model, however, is constrained by underlying equi-dispersion assumption for count data (i.e., that variance mean equal). This work instead introduces flexible contain over- or under-dispersion via Conway-Maxwell-Poisson (CMP) distribution related d...