Abstract

A new Topp–Leone generated family of distributions, which we call the Topp–Leone Discrete Laplace (\(TL-DL\)) distribution, is proposed. It has a shape parameter \(\alpha>0\) and a scale parameter \(0<p<1\). The \(TL-DL\) is an alternative distribution for discrete data that have an asymmetric distribution. Some mathematical properties of the proposed distribution are also derived. Namely, we present the quantile function and the moments for the \(TL-DL\) distribution. The Maximum Likelihood procedure is applied for parameter estimation. An application study is presented using real data. We use two data sets for this part of the analysis to illustrate the applications of the \(TL-DL\) distribution. For the first data set, the change of the stock price in comparison with the closing price for the previous day is considered. The second data set provides information about the comparison of production cycle times of employees before and after the improvement a slippery production line in the degreasing alkaline process by increasing the pressure of the nozzle. The \(TL-DL\) distribution is applied to a real life data and it fits data more efficiently than the Discrete Laplace (\(DL\)) and Discrete Normal (\(DN\)) distributions.

中文翻译：

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Topp-Leone离散拉普拉斯分布及其应用

摘要

提出了新的Topp–Leone生成的分布族，我们称为Topp–Leone离散拉普拉斯（\（TL-DL \））分布。它具有形状参数\（\ alpha> 0 \）和比例参数\（0 <p <1 \）。的\（TL-DL \）是针对具有非对称分布的离散数据的替代分布。还推导了所建议分布的一些数学性质。即，我们给出分位数函数和\（TL-DL \）分布的矩。将最大似然过程应用于参数估计。应用研究是使用实际数据进行的。在此部分的分析中，我们使用两个数据集来说明\（TL-DL \）的应用分配。对于第一个数据集，考虑了股价与前一天收盘价相比的变化。第二个数据集提供了有关在员工进行改进之前和之后的生产周期时间比较的信息，该过程是通过增加喷嘴的压力在脱脂碱性工艺中的湿滑生产线进行的。的\（TL-DL \）分配被应用到实际生活中的数据并将其比离散拉普拉斯（更有效地适合数据\（DL \） ）和离散正常（\（DN \） ）的分布。