MOMENTS OF ORDER STATISTICS AND K-RECORD VALUES ARISING FROM THE BETA-LOMAX DISTRIBUTION WITH APPLICATION

Year 2026, Volume: 16 Issue: 1, 73 - 93, 08.01.2026

Ashwaq Abdulsada Kadhim Alakraa Ali Akbar Heydari Hossein Jabbari Khamnei , Somayeh Makouei

Abstract

The concept of $k$-record values plays a significant role in extreme value theory, which is essential for modeling rare events. In this paper, we focus on $k$-record values from the Beta-Lomax distribution($BLD$), a flexible probability distribution widely used to model extreme events in various fields. We begin by introducing the $BLD$, highlighting its key properties and characteristics. We then define the notion of $k$-record values, which represent the maximum of $k$ consecutive observations from a given dataset. The $k$-record values provide valuable insights into the extreme behavior of the data and are particularly useful for estimating tail probabilities and quantiles. Next, we discuss the statistical properties of $k$-record values from the $BLD$, including their moments, distributional properties, and asymptotic behavior. We explore various methodologies for estimating the parameters of the $BLD$ using maximum likelihood estimation ($MLE$) and discuss strategies for validating the goodness-of-fit of the resulting models. Furthermore, we present applications of $k$-record values from the $BLD$ in real-world scenarios. These include assessing the risk associated with extreme events, such as natural disasters or financial market crashes, and making informed decisions regarding prevention, mitigation, or insurance coverage. Finally, we conclude by summarizing the key findings and contributions of this study. The analysis of $k$-record values from the $BLD$ provides valuable insights into extreme event modeling and enhances our understanding of rare occurrences. The results presented in this paper can help practitioners in diverse fields accurately assess and manage risks associated with extreme events, leading to more robust decision-making processes.

Keywords

Beta-Lomax distribution , k-record values , order statistics , MLE , extreme value theory.

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