On the second record derivative of a sequence of exponential random variables
| Autor: | Valery B. Nevzorov, Alexei Stepanov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Independent and identically distributed random variables
Sequence General Mathematics 010102 general mathematics General Physics and Astronomy Derivative 01 natural sciences 010305 fluids & plasmas Exponential function Combinatorics Distribution (mathematics) 0103 physical sciences Limit (mathematics) 0101 mathematics Random variable Mathematics |
| Zdroj: | Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy. 7:69-76 |
| ISSN: | 2587-5884 1025-3106 |
| DOI: | 10.21638/11701/spbu01.2020.107 |
| Popis: | Let Zi (i ≥ 1) be a sequence of independent and identically distributed random variables with standard exponential distribution H and let Z(n) (n ≥ 1) be the corresponding sequence of exponential records associated with Zi (i ≥ 1). Let us call the sequence Z(n) (n ≥ 1) the first “record derivative” of the sequence Zi (i ≥ 1). ν1 = Z(1). It is known that ν2 = Z(2) – Z(1), independent variables with distribution H. Let T(n) (n ≥ 1) be record times in the sequence ν1, ν2, … while Y(n) = Z(T(n)) and W(n) = Y(n) – Y(n – 1) (n ≥ 1). Let us call the sequence Y(n) (n ≥ 1) (which is the main objective of this research) the second “record derivative” of the sequence Zi (i ≥ 1). We derive the distributions of T(n), Y(n), W(n) and search for the Laplace transform of Y(n) in this paper. A limit result for the sequence Y(n) (n ≥ 1) is obtained, and methods of generation of T(n) and Y(n) are proposed. |
| Databáze: | OpenAIRE |
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