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 -