标题： Lambert W 函数在威布尔分布和非威布尔分布模拟中的应用 显示英文标题

标题： Use of Lambert W function in the simulation of Weibull and non-Weibull distributions

摘要： 在这项工作中，我们研究了一些分布，主要是威布尔分布族，其分位数函数无法通过传统的反演法获得。 我们仅使用反演法，结合超越函数（如Lambert W函数）的帮助，解决了相同的分位数函数。 Lambert W函数的使用帮助了许多领域中的数学模型得到了显式解，而在此之前，这些模型要么没有显式解，要么只能通过近似方法求解。 显示英文摘要

摘要： In this work, we have taken up some distributions, mostly Weibull family, whose quantile functions could not be obtained using the traditional inversion method. We have solved the same quantile functions by using the inversion method only, with the additional help of transcendental functions like the Lambert W function. The usage of the Lambert W function has helped derive closed-form solutions for mathematical models in many fields, for which explicit or exact solutions were not available and approximation was the only known way of approaching it.