93 research outputs found
Characterizations of Student's t-distribution via regressions of order statistics
Utilizing regression properties of order statistics, we characterize a family
of distributions introduced by Akhundov, Balakrishnan, and Nevzorov (2004),
that includes the t-distribution with two degrees of freedom as one of its
members. Then we extend this characterization result to t-distribution with
more than two degrees of freedom.Comment: To appear in "Statistics
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
Simulation and Robust Modifications of Estimates in Branching Processes
This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.This paper is supported by National Foundation for Scienti c Investigation - Bulgaria, grant MM-1101/2001 and PRO-ENBIS: GTC1-2001-43031
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
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
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