On moments of the unit Lindley distribution

Saralees Nadarajah; Stephen Chan

doi:10.1080/02664763.2019.1675607

On moments of the unit Lindley distribution

J Appl Stat. 2019 Oct 9;47(5):947-949. doi: 10.1080/02664763.2019.1675607. eCollection 2020.

Authors

Saralees Nadarajah¹, Stephen Chan²

Affiliations

¹ School of Mathematics, University of Manchester, Manchester, UK.
² Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE.

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: 62E; Incomplete gamma function; Lindley; closed form; exponential integral; incomplete moments.