Alsadat Najwan
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh, 11587, Saudi Arabia.
Heliyon. 2024 Sep 19;10(19):e38143. doi: 10.1016/j.heliyon.2024.e38143. eCollection 2024 Oct 15.
Data analysis is indeed quite popular and crucial in various fields such as meteorology, hydrology, epidemiology, economics, and biology. So, the purpose of this study is to introduce a new probability distribution to analyze rainfall data. A new extension of XLindley distribution is introduced using the alpha power transformation technique. The new distribution is named "alpha power transformed XLindley - (APTXL) distribution". Mathematical properties of APTXL distribution are derived such as ordinary moments, moment generating function, quantile function, mean residual life function, and order statistics. The model parameters are estimated using five different estimation methods such as maximum likelihood, Anderson Darling, Cramer von Misses, Ordinary least squares, and weighted least squares. A comprehensive simulation study is utilized to check the behavior and efficiency of the derived estimators. It is found that the weighted least square approach efficiently estimates the model parameter than the other methods. This derivation of a new model not only contributes to theoretical advances in statistical methodology but also provides practical methods for rainfall data modeling. The APTXL distribution is used to evaluate rainfall datasets from Saudi Arabia. It is identified that the APTXL distribution provides efficient results as compared to considered competitive distributions.
数据分析在气象学、水文学、流行病学、经济学和生物学等各个领域确实非常流行且至关重要。因此，本研究的目的是引入一种新的概率分布来分析降雨数据。使用α幂变换技术引入了XLindley分布的一种新扩展。新分布被命名为“α幂变换XLindley - （APTXL）分布”。推导了APTXL分布的数学性质，如普通矩、矩生成函数、分位数函数、平均剩余寿命函数和顺序统计量。使用最大似然法、安德森 - 达林法、克拉默 - 冯 - 米塞斯法、普通最小二乘法和加权最小二乘法等五种不同的估计方法估计模型参数。利用全面的模拟研究来检验所得估计量的性能和效率。发现加权最小二乘法比其他方法能更有效地估计模型参数。这种新模型的推导不仅有助于统计方法的理论进步，还为降雨数据建模提供了实用方法。APTXL分布用于评估沙特阿拉伯的降雨数据集。结果表明，与所考虑的竞争分布相比，APTXL分布能提供更有效的结果。
