On moments of the unit Lindley distribution

ABSTRACT

Mazucheli et al. [On the one parameter unit-Lindley distribution and its associated regression model for proportion data. J. Appl. Stat. 46 (2019), pp. 700–714] introduced the unit Lindley distribution. The expressions given for the moments and incomplete moments are either not correct or not in closed form. We derive closed form expressions moments and incomplete moments. The expressions are elementary except for the exponential integral.

KEYWORDS:

• Incomplete gamma function
• incomplete moments
• Lindley
• exponential integral
• closed form

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62E

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On the one parameter unit-Lindley distribution and its associated regression model for proportion data

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Acknowledgments

The authors would like to thank the Editor and the two referees for careful reading and comments which greatly improved the paper.

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No potential conflict of interest was reported by the authors.