Yao's formula is one of the basic tools in any situation where one wants to estimate the number of blocks to be read in answer to some query. We show that such situations can be modelized by probabilistic urn models. This allows us to fully characterize the distribution probability of the number of selected blocks under uniformity assumptions, and to consider extensions to non-uniform block pro...

This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2, . . . , n− 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition a...

This work is devoted to the analysis of the area under certain lattice paths. The lattice paths of interest are associated to a class of 2 × 2 triangular Pólya-Eggenberger urn models with ball replacement matrix M = (−a 0 c −d ) , with a, d ∈ N and c = p · a, p ∈ N0. We study the random variable counting the area under sample paths associated to these urn models, where we obtain a precise recur...

Context: It is challenging to develop comprehensive, consistent, analyzable requirements models for evolving requirements. This is particularly critical for certain highly interactive types of socio-technical systems that involve a wide range of stakeholders with disparate backgrounds; system success is often dependent on how well local social constraints are addressed in system design. Objecti...

In this paper, we consider a Pólya urn model containing balls of m different labels under a general replacement scheme, which is characterized by an m×m addition matrix of integers without constraints on the values of these m integers other than non-negativity. This urn model includes some important urn models treated before. By a method based on the probability generating functions, we conside...

A generalised urn model is presented in this paper. The urn contains L different types of balls and its replacement policy depends on both an urn function and a random environment. We consider the Ldimensional stochastic process {Xn} that represents the proportion of balls of each type in the urn after each replacement. This process can be expressed as a stochastic recurrent equation that fits ...