In this paper, the maximum likelihood and Bayesian estimation of the parameters of location-scale Rayleigh distribution with partly interval censored data is considered. For computing the maximum likelihood estimators with partly interval censored data, three methods are used, namely, Newton-Raphson, Expectation-Maximization and Monte-Carlo Expectation-Maximization algorithms. The standard errors of the estimates are computed using the observed information matrix. Also, two types of confidence intervals are constructed using the Wald method and the nonparametric percentile bootstrap confidence intervals. For computing the Bayes estimators, three methods viz Lindley's approximation, Tierney-Kadane approximation and importance sampling methods are used. Highest posterior density (HPD) credible intervals of the two parameters are constructed using importance sampling technique. Monte-Carlo simulation experiments are conducted to investigate the performance of the proposed methods. Finally, the methods are illustrated by using two real data sets, one is related with diabetic patients data set and the other is related to HIV infection data set.

本文考虑了具有部分区间删失数据的位置尺度瑞利分布参数的最大似然和贝叶斯估计。为了计算具有部分区间删失数据的最大似然估计量，使用了三种方法，即Newton-Raphson、期望-最大化和Monte-Carlo 期望-最大化算法。估计的标准误差是使用观察到的信息矩阵计算的。此外，使用 Wald 方法和非参数百分位数 bootstrap 置信区间构建了两种类型的置信区间。为了计算贝叶斯估计量，使用了三种方法，即 Lindley 近似、Tierney-Kadane 近似和重要性采样方法。两个参数的最高后验密度 (HPD) 可信区间是使用重要性采样技术构建的。进行蒙特卡罗模拟实验以研究所提出方法的性能。最后，通过使用两个真实数据集来说明这些方法，一个与糖尿病患者数据集相关，另一个与 HIV 感染数据集相关。