A Higher Moment for Spatial Statistics

Higher Moment Analysis of a Spatial Stochastic Process Algebra

We introduce a spatial stochastic process algebra called MASSPA, which provides a formal behavioural description of Markovian Agent Models, a spatial stochastic modelling framework. We provide a translation to a master equation which governs the underlying transition behaviour. This provides a means of simulation and thus comparison of numerical results with simulation that was previously not a...

A Moment Problem for Order Statistics

Necessary and sufficient conditions are given for a triangular array of numbers to be expectations of order statistics of some nonnegative random variable. Using well-known recurrence relations, the expectations of all order statistics of the largest sample size, n, in the triangular array, or the expectations of the smallest of every sample size up to and including n are sufficient to determin...

Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

Introduction to Higher Order Spatial Statistics in Cosmology

Exponential and Moment Inequalities for U-statistics

A Bernstein-type exponential inequality for (generalized) canonical U -statistics of order 2 is obtained and the Rosenthal and Hoffmann-Jørgensen inequalities for sums of independent random variables are extended to (generalized) U -statistics of any order whose kernels are either nonnegative or canonical.