22 research outputs found
Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes
2000 Mathematics Subject Classification: 60J80, 60G70.We obtain a limit theorem for the row maximum of a triangular array of bivariate geometric random vectors. An application of this limit theorem is provided for maximum family size within a generation of a bisexual branching process with varying geometric offspring laws.This paper is partly supported by NFSI-Bulgaria, Grant No. MM-1101/2001
Subcritical Randomly Indexed Branching Processes
2000 Mathematics Subject Classification: 60J80, 62P05.The paper continues the study of the randomly indexed branching processes in the subcritical case. The asymptotic behavior of the moments and the probability for non-extinction is investigated. Conditional limiting distributions are obtained.The first author wish to thank the Organizing Committee of the ISCPS, SDA, and WBPA 2010 for the financial support which allows him to participate in the conference
An Estimate of the Probability Pr(X<Y)
2000 Mathematics Subject Classification: 33C90, 62E99In the area of stress-strength models there has been a large amount of work as regards estimation of the probability R = Pr(X<Y) when X and Y are independent random variables belonging to the same univariate family of distributions. In this paper we propose an estimate of this quantity based on a simple property of the uniform distribution. We illustrate the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta).The third author is supported by by NFSI-Bulgaria, Grant No. MM-1101/2001
Branching Stochastic Processes: Regulation, Regeneration, Estimation, Applications
2000 Mathematics Subject Classification: 60J80.This is a survey of the works of Bulgarian mathematicians in the area of Branching Stochastic Processes
Limiting Distributions for Lifetimes in Alternating Renewal Processes
2000 Mathematics Subject Classification: 60K05The spent life time and the residual life time are well investigated characteristics of an ordinary renewal process. In the present paper a generalization of these lifetime processes associated with an alternating renewal process is considered. Limiting distributions are presented in the case of in finite mean renewal periods.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001
Extremes of geometric variables with applications to branching processes
We obtain limit theorems for the row extrema of a triangular array of
zero-modified geometric random variables. Some of this is used to obtain limit
theorems for the maximum family size within a generation of a simple branching
process with varying geometric offspring laws.Comment: 12 pages, some proofs are added to the published versio
Extremal and additive processes generated by Pareto distributed random vectors
Pareto distributions are most popular for modeling heavy tailed data. Here, we obtain weak limits of a sequence of extremal and a sequence of additive processes constructed by a series of Bernoulli point processes with bivariate Pareto space components. For the limiting processes we derive the one dimensional distributions in explicit forms. Some of the main properties of these distributions are also proved