标题： 三参数M-Wright分布的推断及其应用 显示英文标题

标题： Inference for three-parameter M-Wright distributions with applications

摘要： 我们提出了针对由Wright函数生成的三参数（位置、尺度和分数参数）变异分布的点估计量。我们还提供了在某些条件下对这些点估计量的不确定性量化程序。这一密度类包括三参数单侧分布和三参数对称双峰$M$-Wright分布族。单侧族自然推广了Airy模型和半正态模型。对称类包括对称Airy模型以及正态或高斯密度。当位置参数为零时，所提出的尺度参数区间估计量在性能上优于\cite{cah12}中推导出的估计量。我们得到了尺度参数和分数参数估计量的渐近协方差结构，这允许相关性的估计。区间估计量的覆盖概率在某种程度上依赖于所提出的定位参数估计量。对于对称情况，样本均值（或中位数）比中位数（或均值）更优，特别是在分数参数大于（或小于）0.39106时，依据它们的渐近相对效率。所提出的估计算法使用合成数据进行了测试，并与它们的自助法对应物进行了比较。所提出的方法论在年龄和身高数据上进行了演示。 显示英文摘要

摘要： We propose point estimators for the three-parameter (location, scale, and the fractional parameter) variant distributions generated by a Wright function. We also provide uncertainty quantification procedures for the proposed point estimators under certain conditions. The class of densities includes the three-parameter one-sided and the three-parameter symmetric bimodal $M$-Wright family of distributions. The one-sided family naturally generalizes the Airy and half-normal models. The symmetric class includes the symmetric Airy and normal or Gaussian densities. The proposed interval estimator for the scale parameter outperformed the estimator derived in \cite{cah12} when the location parameter is zero. We obtain the asymptotic covariance structure for the scale and fractional parameter estimators, which allows estimation of the correlation. The coverage probabilities of the interval estimators slightly depend on the proposed location parameter estimators. For the symmetric case, the sample mean (or median) is favored than the median (or mean) when the fractional parameter is greater (or lesser) than 0.39106 in terms of their asymptotic relative efficiency. The estimation algorithms were tested using synthetic data and were compared with their bootstrap counterparts. The proposed inference procedures were demonstrated on age and height data.