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A new distribution on (0, 1), generalized Log-Lindley distribution, isproposed by extending the Log-Lindley distribution. This new distribution isshown to be a weighted Log-Lindley distribution. Important probabilistic andstatistical properties have been derived. An interesting characterization ofthe weighted distribution in terms of Kullback-Liebler distance and weightedentropy has also been obtained. A useful result in insurance for the distortedpremium principal is presented and verified with numerical calculations. Newregression models for bounded responses based on this distribution and theirapplication is illustrated by considering modeling a real life data on riskmanagement and another data set on outpatient health expenditure in comparisonwith beta regression and Log-Lindley regression models. Much better fits forboth data sets justify the relevance of the new distribution in statisticalmodeling and analysis. Furthermore this generalization, apart from addingflexibility for modelling, retains the compactness and tractability ofstatistical quantities required for statistical analysis, which is a feature ofthe Log-Lindley distribution. Thus, the generalized Log-Lindley distributionshould be a useful addition to statistical models for practitioners.

A new probability model with support on unit interval: Structural properties, regression of bounded response and applications