A new alternative unit- Lindley distribution with increasing failure rate

Document Type : Article


1 Department of Statistics, Faculty of Science, Selcuk University, Konya, 42250, Turkey

2 Department of Measurement and Evaluation, Artvin Coruh University, City Campus, Artvin, 08000, Turkey

3 LMNO, University of Caen-Normandie, Caen, 14032, Fran

4 Department of Mathematical and Statistical Sciences, Marquette University, USA


In this paper, a new one-parameter distribution is proposed by unitizing the Lindley distribution through the hyperbolic tangent transformation. The goal is to map the functionality of the Lindley distribution on the unit interval, with the perspective of offering a new modeling option for treating unit data. In the first part, we provide the motivations and some mathematical properties of the new distribution. Two truncated moments and hazard rate functions are used to characterize the distribution. The emphasis is then switched to its statistical characteristics. Several methods are used to discuss the point estimation of the parameter. The related bias and mean squared error behavior is tested using Monte Carlo simulations for a range of sample sizes. To demonstrate the ability of the model to fit real data, distributional analyses are given.


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