Sharma Vikas Kumar, Singh Sudhanshu V, Shekhawat Komal
Department of Statistics, Institute of Science, Banaras Hindu University (BHU), Varanasi, India.
Department of Mathematics, Institute of Infrastructure, Technology, Research and Management (IITRAM), Ahmedabad, India.
J Appl Stat. 2020 Aug 31;49(2):371-393. doi: 10.1080/02664763.2020.1813694. eCollection 2022.
This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress-strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.
本文介绍了一种双参数指数化泰西耶分布。该分布的主要优点是其风险率函数具有递增、递减和浴盆形状。推导了普通矩、可识别性、分位数、顺序统计量的矩、平均剩余寿命函数和熵测度的表达式。利用分位数探讨了该分布的偏度和峰度。为了研究两个独立随机变量，讨论了应力-强度可靠性和随机序。构造了基于似然、最小二乘、加权最小二乘和乘积间距的估计量，用于估计该分布的未知参数。提出了一种从该分布生成随机样本的算法。进行了模拟实验，以比较所考虑的参数估计量和百分位数的性能。使用所提出的分布对三组实际数据进行拟合，并与竞争分布进行比较。
