In this study, the estimation of parameters of a three-parameter flexible reduced logarithmic-inverse Lomax (FRL-IL) distribution based on progressive type-II right censored sample is studied. These methods include maximum likelihood estimations (MLEs) and Bayesian estimators. Approximate confidence intervals (ACIs) for the reliability and hazard functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs). In addition, two bootstrap CIs are also proposed.

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... Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and linear-exponential (LINEX) loss functions. The Gibbs within Metropolis-Hasting sampler procedure is applied using the Markov Chain Monte Carlo (MCMC) technique to get the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real-life dataset that represents a group of patients with bladder cancer is considered an application of the proposed methods.