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- Characterizations (3)
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- Branching processes (1)
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Articles 1 - 6 of 6
Full-Text Articles in Probability
Long-Term Behavior Of Subordinated Branching Processes With Prevailing Emigration, George Yanev
Long-Term Behavior Of Subordinated Branching Processes With Prevailing Emigration, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
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.
On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev
On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.
Controlled Branching Processes With Continuous Time, Miguel Gonzalez, Manuel Molina, Ines Del Puerto, Nikolay Yanev, George Yanev
Controlled Branching Processes With Continuous Time, Miguel Gonzalez, Manuel Molina, Ines Del Puerto, Nikolay Yanev, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.
Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco
Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco
School of Mathematical & Statistical Sciences Faculty Publications
Controlled branching processes with continuous time are introduced and limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
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 ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’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 …
On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.