This work deals with the estimation of parameters of Mittag-Leffler (ML($α, σ$)) distribution. We estimate the parameters of ML($α, σ$) using empirical Laplace transform method. The simulation study indicates that the proposed method provides satisfactory results. The real life application of ML($α, σ$) distribution on high frequency trading data is also demonstrated. We also provide the estimation of three-parameter Mittag-Leffler distribution using empirical Laplace transform. Additionally, we establish an autoregressive model of order 1, incorporating the Mittag-Leffler distribution as marginals in one scenario and as innovation terms in another. We apply empirical Laplace transform method to estimate the model parameters and provide the simulation study for the same.

翻译：本研究致力于米塔格-莱夫勒分布（ML($α, σ$)）的参数估计。我们采用经验拉普拉斯变换方法对ML($α, σ$)的参数进行估计。仿真研究表明，所提方法能取得令人满意的结果。本文同时展示了ML($α, σ$)分布在高频交易数据中的实际应用。此外，我们利用经验拉普拉斯变换给出了三参数米塔格-莱夫勒分布的估计方法。在此基础上，我们构建了一阶自回归模型：在一种设定中将米塔格-莱夫勒分布作为边缘分布，在另一种设定中将其作为创新项。我们应用经验拉普拉斯变换方法对模型参数进行估计，并提供了相应的仿真研究。