Optimal interval estimation for a family of lower truncated distribution under progressive censoring

In this paper, based on progressively Type-II censored sample, different types of interval estimates of a general lower truncated distribution are constructed. Exact confidence intervals and joint exact confidence regions are derived for unknown model parameter and the lower truncated threshold bound. Optimal criteria are also provided for choosing the best confidence interval and confidence region among obtained estimates. Two real-life examples and a numerical study are presented to illustrate the performance of our results.