复合型线性失效率-幂级数分布：模型、性质及应用
The Compound Class of Linear Failure Rate-Power Series Distributions: Model, Properties and Applications
摘要：
本文引入了一类新的分布，它推广了线性失效率（LFR）分布，并将LFR分布与幂级数（PS）分布复合得到。这类新的分布被称为线性失效率-幂级数（LFRPS）分布，它包含了一些新的分布，如线性失效率几何（LFRG）分布、线性失效率泊松（LFRP）分布、线性失效率对数（LFRL）分布、线性失效率二项（LFRB）分布和Raylight-power series（RPS）分布。一些前人的工作，如指数幂级数（EPS）类的分布，指数几何（EG）分布，指数泊松（EP）分布和指数对数（EL）分布是新提出的模型的特殊情况。LFRPS类分布的能力在于覆盖五种可能的风险率函数，即，渐增、渐减、倒置浴缸（单峰）、渐减浴缸和渐增形。本文讨论了LFRPS分布的矩、EM算法的极大似然估计和大样本下的推断等性质。为了展示新分布类的灵活性和潜力，利用一个实际数据集比较了新分布类及其部分子模型的拟合结果。
英文摘要：
We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model. The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
