The beta-Lindley distribution: properties and applications. (English) Zbl 1437.62083
Summary: We introduce the new continuous distribution, the so-called beta-Lindley distribution that extends the Lindley distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the \(r\) th moment thus, generalizing some results in the literature. Expressions for the density, moment generating function, and \(r\) th moment of the order statistics also are obtained. Further, we also discuss estimation of the unknown model parameters in both classical and Bayesian setup. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modelling positive real data in many areas.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62E10 | Characterization and structure theory of statistical distributions |
| 62N05 | Reliability and life testing |
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