On the number and sum of near-record observations

On the number and sum of near-record observations

Let X 1,X 2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables X i as near-nth-record observations if X i ∈(X(n)-a,X(n...

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Veröffentlicht in:Advances in applied probability 2005-09, Vol.37 (3), p.765-780
Hauptverfasser: Balakrishnan, N., Pakes, A.G., Stepanov, A.
Format: Artikel
Sprache:eng
Schlagworte:
60G70
62G30
Distribution functions
General Applied Probability
insurance claim
Insurance claims
Integrands
limit theorem
Mathematical theorems
Mathematics
Natural numbers
near-record observation
Perceptron convergence procedure
Probability
Random variables
Record
record time
Studies
sum of near-record observations
Variables
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Beschreibung
Zusammenfassung:Let X 1,X 2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables X i as near-nth-record observations if X i ∈(X(n)-a,X(n)], with a>0, and L(n)
ISSN:0001-8678
1475-6064
DOI:10.1239/aap/1127483746