一类广义威布尔分布及应用

A Class of Generalized Weibull Distribution and Its Application

文章在置换威布尔分布的基础上,通过添加一个形状参数构造了一类修正的威布尔分布。使用广义牛顿二项式展开技巧,研究了新模型的各种结构性质,包括分布函数、密度函数、风险函数、分位数、矩和条件矩、剩余寿命函数以及两种不同熵的解析表达式,使用极大似然法给出了模型的参数估计。实证结果表明,新提出的模型拟合效果最优。

This paper constructs a modified Weibull distribution by adding a shape parameter on the basis of permutation Weibull distribution.Then the paper uses the technique of generalized Newtonian binomial expansion to study various structural properties of the new model,including analytic expressions for cumulative distribution function,probability density function,hazard rate function,quantile function,moment and conditional moment,residual life functions and two different entropies.Finally,the paper employs the method of maximum likelihood to estimate the parameters of the model.Empirical results show that the newly posed model have the best fitting effect.