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George P. Yanev

Publications and source records attributed to George P. Yanev.

At least 19 recordsLinked to original sources
arXiv2025

Long-Term Behavior of Subordinated Branching Processes with Prevailing Emigration

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination mechanism, involving renewal processes. The key findings highlight how the initial population size and the interarrival mean time influence both asymptotic behavior of the non-extinction probability and corresponding Yaglom type limit theorems. We also study an alternating regenerative process, when the population cycles between zero and positive states. This research complements previous studies for processes when immigration prevails over emigration.

math.PR↗
arXiv2020

Exponential and Hypoexponential Distributions: Some Characterizations

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some $n\ge 2$, $X_1, X_2,\,\ldots,\,X_n$ are independent copies of a random variable $X$ with unknown distribution $F$ and a specific linear combination of $X_j$'s has hypoexponential distribution, then $F$ is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.

math.PR↗
arXiv2017

Characterization of exponential distribution through bivariate regression of record values revisited

It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record values, one previous and one future, as covariates. The underlying distribution is exponential if and only if the above regression equals the expected value of an appropriately defined Beta distributed random variable. In a particular case, the expected value of the Beta variable reduces to a weighted average of the covariates.

math.PR↗
arXiv2017

Characterizations of Exponential Distribution Based on Two-Sided Random Shifts

A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a recently developed technique including the Maclaurin series expansion of the probability density of the parent variable.

math.PR↗
arXiv2014

Critical Controlled Branching Processes and Their Relatives

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.

math.PR↗
arXiv2013

Time to Extinction in Subcritical Two-Sex Branching Processes

Lower and upper bounds for the cumulative distribution function (cdf) of the time to extinction in a subcritical two-sex branching process are derived. A recursive procedure for approximating this cdf is also utilized. The results are illustrated with some simulations.

math.PR↗
arXiv2011

Characterizations of distributions via order statistics with random exponential shifts

A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions is obtained. The results extend some known characterizations of exponential and logistic distributions.

math.PR↗
arXiv2011

Characterization of exponential distribution via regression of one record value on two non-adjacent record values

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the other next to the fixed record value, and none of them are adjacent. In particular, it turns out that the underlying distribution is exponential if and only if given the first and last record values, the expected value of the median in a sample of record values equals the sample midrange.

math.PR↗
arXiv2010

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.

math.PR↗
arXiv2007

Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.

math.PR↗
arXiv2006

Revisiting Offspring Maxima in Branching Processes

We present a progress report for studies on maxima related to offspring in branching processes. We summarize and discuss the findings on the subject that appeared in the last ten years. Some of the results are refined and illustrated with new examples.

math.PR↗