A New Extension of the Topp–Leone-Family of Models with Applications to Real Data

In this article, we proposed a new extension of the Topp–Leone family distributions. Some important properties model are developed, such as quantile function, stochastic ordering, series representation, moments, stress–strength reliability parameter, Renyi entropy, order statistics, and moment residual life. A particular member called extended exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square (LSE), percentile (PE) used for parameter estimation. Simulation studies were conducted using NETLE to assess MLE, LSE, PE performance by examining their bias mean square error (MSE), result was satisfactory. Finally, applications two real data sets provided illustrate importance NETLG families in practice; consist daily deaths due COVID-19 California New Jersey, USA. The outperformed many other existing Topp–Leone’s related distributions based on illustrations.