离散alpha偏正态分布:性质和参数估计

Discrete Alpha Skew Normal Distribution:Properties and Parameter Estimation

为了获得新的概率模型处理离散寿命数据或可数数据,首次提出了包含离散正态分布的离散alpha偏正态分布,给出了该分布的矩、生存函数和失败率函数,研究了该分布参数的最大似然估计。通过随机模拟试验讨论估计量的优良性,模拟结果表明:参数最大似然估计的均方误差和标准差随着样本量的增大而减小,最后将该分布对125例髓母细胞癌患者年龄数据集进行拟合,发现离散alpha偏正态分布比alpha偏正态分布具有更好的拟合效果。

In this paper,a discrete alpha skew normal distribution which includes discrete normal distribution is proposed in order to obtain a new probability model to deal with discrete life data or countable data,the moment,survival function and failure rate function of the distribution are obtained,and the maximum likelihood estimation of the parameters is studied.Moreover,the random simulations are carried out for discussing the performance of the estimators,simulation results show that the mean square error and standard deviation of maximum likelihood estimators decrease with the increase of sample size.Finally,we use the distribution to fit the age data set of 125 patients with medulloblastoma,and find that the discrete alpha skew normal distribution has better fitting effect than the alpha skew normal distribution.