We introduce a new distribution for modeling extreme events about frequency analysis called modified Burr IV (MBIV) distribution. We derive the MBIV distribution on the basis of the generalized Pearson differential equation. The proposed model turns out to be flexible: its density function can be symmetrical, right-skewed, left-skewed, J and bimodal shaped. Its hazard rate has shapes such as bathtub and modified bathtub, increasing, decreasing, and increasing-decreasing-increasing. To show the importance of the MBIV distribution, we establish various mathematical properties such as random number generator, sub-models, moments related properties, inequality measures, reliability measures, uncertainty measures and characterizations. We utilize the maximum likelihood estimation technique to estimate the model parameters. We assess the behavior of the maximum likelihood estimators (MLEs) of the MBIV parameters via a simulation study. Five data sets related to frequency analysis are considered to elucidate the significance of the MBIV distribution. We show that the MBIV model is the best model to analyze data for hydrological events, motivating its high level of adaptability in the applied setting.

我们引入了一种新的分布，用于对频率分析的极端事件进行建模，称为修正 Burr IV (MBIV) 分布。我们基于广义 Pearson 微分方程推导出 MBIV 分布。所提出的模型被证明是灵活的：它的密度函数可以是对称的、右偏斜的、左偏斜的、J 形和双峰形。其危害率有浴缸和改良浴缸等形状，增加、减少、增加-减少-增加。为了展示 MBIV 分布的重要性，我们建立了各种数学属性，例如随机数生成器、子模型、矩相关属性、不等式度量、可靠性度量、不确定性度量和表征。我们利用最大似然估计技术来估计模型参数。我们通过模拟研究评估 MBIV 参数的最大似然估计量 (MLE) 的行为。与频率分析相关的五个数据集被认为是阐明 MBIV 分布的重要性。我们表明，MBIV 模型是分析水文事件数据的最佳模型，激发了其在应用环境中的高度适应性。