AT-II PHCS下Gumbel II型分布的参数估计及Covid-19数据的应用
Estimation of parameters of the Gumbel type-II distribution under AT-II PHCS with an application of Covid-19 data
摘要：
本文研究了Gumbel Ⅱ型分布在自适应Ⅱ型渐进混合截尾样本下未知参数的经典估计和贝叶斯估计。最大似然估计（MLE）和最大产品间距估计（MPSE）的发展和数值计算使用牛顿-拉夫逊方法。贝叶斯方法被用来估计对称和非对称损失函数下的参数。贝叶斯估计没有明确的形式。因此，通过使用马尔可夫链蒙特卡罗（MCMC）方法以及Metropolis-Hastings（MH）算法获得贝叶斯估计。基于极大似然估计的正态性，构造了渐近置信区间。构造了Bootstrap区间和最高后验密度（HPD）可信区间。进一步进行了蒙特卡罗模拟研究。最后，分析了基于印度Covid-19死亡率的数据集，以说明目的。
英文摘要：
In this paper, we investigate the classical and Bayesian estimation of unknown parameters of the Gumbel type-II distribution based on adaptive type-II progressive hybrid censored sample (AT-II PHCS). The maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) are developed and computed numerically using Newton-Raphson method. Bayesian approaches are employed to estimate parameters under symmetric and asymmetric loss functions. Bayesian estimates are not in explicit forms. Thus, Bayesian estimates are obtained by using Markov chain Monte Carlo (MCMC) method along with the Metropolis-Hastings (MH) algorithm. Based on the normality property of MLEs the asymptotic confidence intervals are constructed. Also, bootstrap intervals and highest posterior density (HPD) credible intervals are constructed. Further a Monte Carlo simulation study is carried out. Finally, the data set based on the death rate due to Covid-19 in India is analyzed for illustration of the purpose.
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