We propose a new bounded distribution called the Marshall-Olkin reduced Kies distribution, which is a competitive model to the generalized beta, Kumaraswamy and beta distributions. It is able to model both negative and positive skewed data. Eight classical estimation methods are used to estimate its parameters. A simulation study is conducted to compare the performance of the different estimators. The performance ordering of these estimators is explored using partial and overall ranks to determine the best estimation method. Two COVID-19 data sets on to recovering and death rates in Spain are analyzed to show the flexibility of the new distribution to model such data. The expected values of the first and last order statistics are used to estimate the minimum and maximum recovery and death rates.