A new extension of power Lindley distribution for analyzing bimodal data.

*(English)*Zbl 1449.62025Summary: In this article, we introduce a new three-parameter odd log-logistic power Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the parameters. An application of the model to two real data sets is presented finally and compared with the fit attained by some other well-known two and three-parameter distributions for illustrative purposes. It is observed that the proposed model has some advantages in analyzing lifetime data as compared to other popular models in the sense that it exhibits varying shapes and shows more flexibility than many currently available distributions.

##### MSC:

62E15 | Exact distribution theory in statistics |

62N05 | Reliability and life testing |

60E05 | Probability distributions: general theory |

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\textit{M. Alizadeh} et al., Chil. J. Stat. 8, No. 1, 67--86 (2017; Zbl 1449.62025)

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