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Al-Shomrani et al. (2016) introduced a new family of distributions (TL-G) based on the Topp-Leone distribution (TL) by replacing the variable x by any cumulative distribution function G(t). With only one extra parameter which controls the skewness, this family is a good competitor to several generalized distributions used in statistical analysis. In this work, we consider the extended exponential as the baseline distribution G to obtain a new model called the Topp-Leone extended exponential distribution TL-EE. After studying mathematical and statistical properties of this model, we propose different estimation methods such as maximum likelihood estimation, method of ordinary and weighted least squares, method of percentile, method of maximum product of spacing, method of Cramer Von-Mises, modified least squares estimators and chi-square minimum method for estimating the unknown parameters. In addition to the classical criteria for model selection, we develop for this distribution a goodness-of-fit statistic test based on a modification of Pearson statistic. The performances of the methods used are demonstrated by an extensive simulation study. With applications to covid-19 data and waiting times for bank service, a comparison evaluation shows that the proposed model describes data better than several competing distributions.
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