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Full-Text Articles in Physical Sciences and Mathematics
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 and Statistical Sciences Faculty Publications and Presentations
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.
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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 and Statistical Sciences Faculty Publications and Presentations
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.
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.
Characterizations Of Logistic Distribution Through Order Statistics With Independent Exponential Shifts, M. Ahsanullah, George Yanev, Constantin Onica
Characterizations Of Logistic Distribution Through Order Statistics With Independent Exponential Shifts, M. Ahsanullah, George Yanev, Constantin Onica
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts are established. Utilizing these properties, we extend several known results and obtain new characterizations of the logistic distribution.
Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev
Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.