Generalized conditional spacings and their stochastic properties

Tie Li; Zhengcheng Zhang; Tie Li; Zhengcheng Zhang

doi:10.3934/math.20241162

AIMS Mathematics

2024, Volume 9, Issue 9: 23909-23923. doi: 10.3934/math.20241162

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Generalized conditional spacings and their stochastic properties

Tie Li ^1,2,
Zhengcheng Zhang ^{1
,
,}

1.
School of Mathematics and Statistics, Hainan Normal University, 99 South Longkun Road, Haikou, 571158, China
2.
Faculty of Mathematics, Baotou Teachers' College, 3 Science Road, Baotou, 014030, China

Received: 12 June 2024 Revised: 24 July 2024 Accepted: 31 July 2024 Published: 12 August 2024
MSC : 60E15, 62G30

This paper introduces the concept of generalized conditional spacings and establishes partial order relations between different generalized spacings. First, we derive the survival function of the generalized conditional spacings. Second, we construct the stochastic and hazard rate order relationships between different generalized conditional spacings and generalized normal conditional spacings, considering parent distributions that belong to the decreasing failure rate (DFR) and increasing likelihood rate (ILR) classes. Finally, for parent distributions within the DFR class, we obtain the dispersive order between different conditional spacings, along with an inequality for the variance. Additionally, we present illustrative examples involving Pareto and Gamma distributions.
- generalized conditional spacings,
- k-out-of-n systems,
- DFR,
- ILR,
- stochastic order,
- hazard rate order
Citation: Tie Li, Zhengcheng Zhang. Generalized conditional spacings and their stochastic properties[J]. AIMS Mathematics, 2024, 9(9): 23909-23923. doi: 10.3934/math.20241162

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Abstract

This paper introduces the concept of generalized conditional spacings and establishes partial order relations between different generalized spacings. First, we derive the survival function of the generalized conditional spacings. Second, we construct the stochastic and hazard rate order relationships between different generalized conditional spacings and generalized normal conditional spacings, considering parent distributions that belong to the decreasing failure rate (DFR) and increasing likelihood rate (ILR) classes. Finally, for parent distributions within the DFR class, we obtain the dispersive order between different conditional spacings, along with an inequality for the variance. Additionally, we present illustrative examples involving Pareto and Gamma distributions.

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