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The Beta‐Lindley Distribution: Properties and Applications

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  • Faton Merovci
  • Vikas Kumar Sharma

Abstract

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 rth moment thus, generalizing some results in the literature. Expressions for the density, moment generating function, and rth 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.

Suggested Citation

  • Faton Merovci & Vikas Kumar Sharma, 2014. "The Beta‐Lindley Distribution: Properties and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:198951
    DOI: 10.1155/2014/198951
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    References listed on IDEAS

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    2. W. K. Hastings, 1970. "Monte Carlo sampling methods using Markov chains and their applications," Biometrika, Biometrika Trust, vol. 57(1), pages 97-109.
    3. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
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