Progressive Type-II Censored Data and Associated Inference with Application Based on Li–Li Rayleigh Distribution

Based on progressive Type-II censored samples, we first derive the recurrence relations for the single and product moments of progressively Type-II censored order statistics from two parameter Rayleigh distribution. These recurrence relations enable us to compute the mean and variances of all progressively Type-II censored order statistics for all sample sizes in a simple and efficient manner. Further, an algorithm is discussed which enable us to compute all the means and variances of two parameter Rayleigh progressive Type-II censored order statistics for all sample sizes and all censoring schemes. Next, we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the parameters of the Rayleigh distribution. Finally, we consider Bayes estimation under five different types of loss functions (symmetric and asymmetric loss functions) using independent gamma priors for both the unknown parameters. Monte Carlo simulations are performed to compare the performance of the proposed methods, and one data set has been analyzed for illustrative purposes. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.