134 research outputs found
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.Comment: To appear in PLISKA Studia Mathematica Bulgaric
Characterizations of exponential distribution via conditional expectations of record values
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
Variance estimators in critical branching processes with non-homogeneous immigration
The asymptotic normality of conditional least squares estimators for the
offspring variance in critical branching processes with non-homogeneous
immigration is established, under moment assumptions on both reproduction and
immigration. The proofs use martingale techniques and weak convergence results
in Skorokhod spaces.Comment: Accepted for publication in Math Population Studie
Characterizations of Exponential Distribution Based on Sample of Size Three
2010 Mathematics Subject Classification: 62G30, 62E10.Two characterizations of the exponential distribution based on equalities among order statistics in a random sample of size three are proved. This proves two conjectures stated recently in Arnold and Villaseñor [4]
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
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