The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated. Applying the simulation study, the question of selecting the optimal scaling parameter of the proposed Laplace transform inversion is considered. The behavior of the approximants are demonstrated via plots and table.

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关于从指数矩恢复分布的说明

研究了通过标度拉普拉斯变换反演恢复正随机变量累积分布函数的问题。推导出建议近似的统一上限。研究了复合泊松分布的近似值以及给定复合泊松分布样本的被加数分布函数的估计。应用仿真研究，考虑了选择所提出的拉普拉斯变换反演的最佳标度参数的问题。近似值的行为通过绘图和表格进行演示。