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On the Bahadur Representation of Quantiles for a Sample from ρ*-Mixing Structure Population

Dudek Dagmara, Kuczmaszewska Anna

Advances in Science and Technology. Research Journal

2022

Vol. 16, no 3

316--330

In this paper, we establish the strong consistency and the Bahadur representation of sample quantiles for ρ*-mixing random variables. Additionally, the asymptotic normality and the Berry-Esseen bound of sample quantiles for ρ*-mixing random variables are presented. Additionally, we provide the rate of convergence of sample quantiles to population counterparts. Moreover, numerical simulation is presented to ilustrate and verify obtained results.

New Characteristics in the Assessment of Reliability of Machines and Devices

Kopania Gabriela, Kuczmaszewska Anna

Management and Production Engineering Review

2021

Vol. 14, No. 4

45--52

The aim of this work is to present new reliability characteristics expressed as functions of some variable expressing the measure of effective operation of a machine or a device. These characteristics can be used for both renewable and non-renewable objects. Their mathematical idea reflects the essence of already known characteristics, i.e. it expresses the probability of failure but expressed as a function of a variable, not necessarily identified with time.