Some discrete distributions generated by stable densities (DGSDs) could be considered as models for describing phenomena arising in bioinformatics. Since probability mass and distribution functions are not in closed forms, simulation studies and real applications of these distributions have not been studied yet. To do this, we need to consider DGSDs as truncated, namely, truncated DGSDs (T-DGSDs). In this paper, some statistical properties of the T-DGSDs models are established. Based on the Monte Carlo method, limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, and Nelder–Mead optimization algorithms, we do a simulation to estimate biases, mean square errors, and maximum likelihood estimations for the unknown parameters of the T-DGSDs. Moreover, we fit these T-DGSDs models with some real data sets in bioinformatics and then compare them to some frequency distributions.

由稳定密度（DGSD）生成的一些离散分布可以被视为描述生物信息学中出现的现象的模型。由于概率质量和分布函数不是封闭形式，因此尚未研究这些分布的仿真研究和实际应用。为此，我们需要将DGSD视为已删节，即，已删节的DGSD（T-DGSD）。本文建立了T-DGSDs模型的一些统计性质。基于蒙特卡罗方法，有限约束的Broyden-Fletcher-Goldfarb-Shanno有限约束优化和Nelder-Mead优化算法，我们进行了仿真以估计未知参数的偏差，均方误差和最大似然估计T-DGSD的数量。而且，