Conditions for finiteness and bounds on moments of record values from iid continuous life distributions
[ 1 ] Instytut Automatyki i Robotyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] pracownik
[2.2] Automatyka, elektronika, elektrotechnika i technologie kosmiczne
2023
artykuł naukowy
angielski
- Independent identically distributed random variables
- Continuous life distribution
- Record value
- Moment
- Sharp bound
EN We consider the standard and kth record values arising in sequences of independent identically distributed continuous and positive random variables with finite expectations. We determine necessary and sufficient conditions on the type of record k, its number n and moment order r so that the rth moment of the n value of kth record is finite for every parent distribution. Under the conditions we present the optimal upper bounds on these moments expressed in the scale units being the respective powers of the first population moment. The theoretical results are illustrated by some numerical evaluations.
09.11.2022
83 - 100
CC BY (uznanie autorstwa)
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