Wrapped Two-Parameter Lindley Distribution for Modelling Circular Data

Abstract

In this paper, a new circular probability model with two parameters namely, the wrapped two-parameter Lindley distribution is proposed. Behavior of the density function with variation in the values of the parameters is examined and expressions for its characteristic function, trigonometric moments and other related descriptive measures are derived. Operation of wrapping and convoluting linear distribution around a unit circle is investigated. The method of maximum likelihood is used to estimate the unknown parameters of this distribution and a simulation study is conducted to check the consistency of these estimates. Finally, the proposed model is fitted to two real-life circular data sets and the goodness-of-fit of this distribution is assessed in comparison to wrapped exponential and wrapped Lindley distributions to elucidate the modelling potential of the proposed distribution.