This work presents a non-parametric estimator for the cumulative distribution function (CDF) of the jump-size distribution for a storage system with compound Poisson input. The workload process is observed according to an independent Poisson sampling process. The nonparametric estimator is constructed by first estimating the characteristic function (CF) and then applying an inversion formula. The convergence rate of the CF estimator at $s$ is shown to be of the order of $s^2/n$, where $n$ is the sample size. This convergence rate is leveraged to explore the bias-variance tradeoff of the inversion estimator. It is demonstrated that within a certain class of continuous distributions, the risk, in terms of MSE, is uniformly bounded by $C n^{-\frac{\eta}{1+\eta}}$, where $C$ is a positive constant and the parameter $\eta>0$ depends on the smoothness of the underlying class of distributions. A heuristic method is further developed to address the case of an unknown rate of the compound Poisson input process.

翻译：本文针对具有复合泊松输入的存储系统，提出了跳跃大小分布的累积分布函数(CDF)的非参数估计方法。工作负荷过程依据独立泊松采样过程进行观测。该非参数估计量通过先估计特征函数(CF)，再应用反演公式构建。CF估计量在$s$处的收敛速度被证明为$s^2/n$量级，其中$n$为样本量。利用此收敛速度探究反演估计量的偏差-方差权衡。研究表明，在某一类连续分布中，以均方误差(MSE)衡量的风险一致有界于$C n^{-\frac{\eta}{1+\eta}}$，其中$C$为正参数，参数$\eta>0$取决于潜在分布类的光滑性。进一步开发了启发式方法以处理复合泊松输入过程速率未知的情形。