Abstract
In this study we introduce a new extended class of continuous distributions named generalized Lindley family of distributions. Some properties of the new generator, including ordinary moments, quantile, generating and entropy functions, which hold for any baseline model, are presented. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new family of distributions is shown via an application on the wind speed data set. The results shows that the proposed family is better than well-known distributions including log-logistic, Burr, Dagum, Frechet, Pearson, Dagum, Lindley, Weibull and exponential distributions.
Highlights
Probability distributions are very useful in describing and predicting real world phenomena
The rest of the paper is organized as follows: In Section 2, we introduce some special models of the new family
The moments can be obtained using the integral based on quantile functions
Summary
Probability distributions are very useful in describing and predicting real world phenomena. The new distribution becomes more flexible and gives a better fit to the practical data in many areas of study. Among those procedures, the definition of new generators or families of distributions by introducing additional parameter(s) to the baseline distribution is very popular. The probability density function (pdf) of the Lindley distribution with a scale parameter is given by l(x; λ) λ2 (1+ x)e-λx , x > 0, λ > 0 1+ λ (1). In this study, motivated by Cakmakyapan & Ozel (2016), the cdf of the generalized Lindley-G (GL-G in short) family of distributions is obtained as λ -log[1-Fa (x;ξ)] 2.
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