TY - JOUR

T1 - Record values with constraints

AU - Nevzorov, V.B.

PY - 2013

Y1 - 2013

N2 - Record values are very popular in probability and mathematical statistics. There are many books and papers concerned with classical record values and record times, i.e., records in sequences of independent equally distributed random variables. In recent times, new types of record values (records in the Fα-scheme, record values in sequences of unequally distributed random variables, records with confirmations, exceedance record values) have been proposed and examined. The present paper proposes another record scheme (so-called "records with constraint"). Various cases are studied in which these records may be useful. For these record values, we give their joint density functions and discover some of their properties. For particular cases of utmost importance, when the initial random variables are independent and have equal exponential distribution, we obtain fairly simple representations of records with constraints as sums of independent equally distributed random terms. © 2013 Allerton Press, Inc.

AB - Record values are very popular in probability and mathematical statistics. There are many books and papers concerned with classical record values and record times, i.e., records in sequences of independent equally distributed random variables. In recent times, new types of record values (records in the Fα-scheme, record values in sequences of unequally distributed random variables, records with confirmations, exceedance record values) have been proposed and examined. The present paper proposes another record scheme (so-called "records with constraint"). Various cases are studied in which these records may be useful. For these record values, we give their joint density functions and discover some of their properties. For particular cases of utmost importance, when the initial random variables are independent and have equal exponential distribution, we obtain fairly simple representations of records with constraints as sums of independent equally distributed random terms. © 2013 Allerton Press, Inc.

U2 - 10.3103/S1063454113030072

DO - 10.3103/S1063454113030072

M3 - Article

SP - 170

EP - 174

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -