A new extension of Weibull distribution: Properties and different methods of estimation

The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization of the Weibull distribution, called Alpha logarithmic transformed Weibull distribution that provides better fits than some of its known generalizations. The proposed distribution contains Weibull, exponential, logarithmic transformed exponential and logarithmic transformed Weibull distributions as special cases. Our main focus is the estimation from frequentist point of view of the unknown parameters along with some mathematical properties of the new model. The proposed distribution accommodates monotonically increasing, decreasing, bathtub and unimodal and then bathtub shape hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.