In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model.

中文翻译：

---

利用非对称概率函数对极值建模

在本文中，提出了一种新的具有三个参数的灵活概率密度函数，用于对具有不同类型峰态（中峰态、细峰态和侧峰态）的非对称数据（正和负）进行建模。推导出了它的一些统计和可靠性属性，包括危险率函数、矩、矩生成函数、不完全矩、平均偏差、剩余寿命矩、反向剩余寿命矩和阶次统计。它的危险率函数可以是常数、增常数、减常数、U 形、倒置形或倒 U 形。考虑了七种经典估计方法来估计未知模型参数。进行蒙特卡罗模拟实验以比较七种不同估计方法的性能。最后，