Recent studies have pointed out the potential of the odd Fréchet family (or class) of continuous distributions in fitting data of all kinds. In this article, we propose an extension of this family through the so-called “Topp-Leone strategy”, aiming to improve its overall flexibility by adding a shape parameter. The main objective is to offer original distributions with modifiable properties, from which adaptive and pliant statistical models can be derived. For the new family, these aspects are illustrated by the means of comprehensive mathematical and numerical results. In particular, we emphasize a special distribution with three parameters based on the exponential distribution. The related model is shown to be skillful to the fitting of various lifetime data, more or less heterogeneous. Among all the possible applications, we consider two data sets of current interest, linked to the COVID-19 pandemic. They concern daily cases confirmed and recovered in Pakistan from March 24 to April 28, 2020. As a result of our analyzes, the proposed model has the best fitting results in comparison to serious challengers, including the former odd Fréchet model.

General family of distributions; asymmetric distributions; probabilistic properties; parametric estimation; confidence intervals; COVID-19 pandemic; data analysis