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On families of distributions characterized by certain properties of ordered random variables. / Ananjevskii, S. M. ; Nevzorov, V. B. .
в: Vestnik St. Petersburg University: Mathematics, Том 49, № 3, 07.2016, стр. 197-203.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On families of distributions characterized by certain properties of ordered random variables
AU - Ananjevskii, S. M.
AU - Nevzorov, V. B.
N1 - Ananjevskii, S.M., Nevzorov, V.B. On families of distributions characterized by certain properties of ordered random variables. Vestnik St.Petersb. Univ.Math. 49, 197–203 (2016). https://doi.org/10.3103/S106345411603002X
PY - 2016/7
Y1 - 2016/7
N2 - In this work, we obtain new characterizations of certain probability distributions by relations with different ordered random variables. Such variables include order statistics, sequential maxima, and records. We consider relations that include not only upper, but also lower record values. The presented ordered objects are based on sequences of independent random variables with a common continuous distribution function. We also investigate equalities in the distribution of sequential maxima exposed by various random shifts. These shifts (one-sided or two-sided) have exponential distributions. Certain theorems and their corollaries present corresponding characterizations of distributions by relations of such a type. In addition, we consider exponentially shifted order statistics such that simple relations among them also characterize certain probability distributions. All of the presented results yield a set of characterizations of various distributions. For particular cases, we present the relations that characterize families of classical exponential and logistic distributions.
AB - In this work, we obtain new characterizations of certain probability distributions by relations with different ordered random variables. Such variables include order statistics, sequential maxima, and records. We consider relations that include not only upper, but also lower record values. The presented ordered objects are based on sequences of independent random variables with a common continuous distribution function. We also investigate equalities in the distribution of sequential maxima exposed by various random shifts. These shifts (one-sided or two-sided) have exponential distributions. Certain theorems and their corollaries present corresponding characterizations of distributions by relations of such a type. In addition, we consider exponentially shifted order statistics such that simple relations among them also characterize certain probability distributions. All of the presented results yield a set of characterizations of various distributions. For particular cases, we present the relations that characterize families of classical exponential and logistic distributions.
KW - order statistics
KW - sequential maxima
KW - record values
KW - characterizations of probability distributions
KW - exponential distribution
KW - logistic distribution
UR - https://link.springer.com/article/10.3103/S106345411603002X
M3 - Article
VL - 49
SP - 197
EP - 203
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 3
ER -
ID: 9307612