Abstract:
Al-Shomrani et al.(2016)introduced a new family of distributions (T L G) based on the Topp-Leone distribution (T L) by replacing the variable x by any cumulative distribution function G(t). With only one extra parameter which control 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 T L 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 , modi fied 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 severalcompeting distributions.
Keywords:
maximum likelihood estimation
,
method of percentile
,
method of maximum product of spacing
,
method of Cramer VonMises
,
modified least squares estimators