The wrapped Monsef Distribution with Application to Tawaf Data

Abstract

Various forms of rituals based on circular motions either clockwise or anti-clockwise. Tawaf is one of the most important
rituals of the pilgrimage and refers to walk in circles around the Holy Kaabah in an anti-clockwise motion. It’s an act of devotion to bring
the pilgrim closer to Allah spiritually. In this paper, the wrapped Monsef distribution is proposed to model the direction of the pilgrims
at tawaf. The behavior of the density function with changing parameter values is investigated and expressions for its characteristic
function, trigonometric moments, and other related circular measures are derived. Maximum likelihood estimation is used to estimate
parameters. A simulation analysis is conducted to demonstrate that the resulting ML estimator is accurate. Finally, the proposed model
is tested using three real-life datasets. Its performance is compared with some wrapped distributions to examine its flexibility and it’s
found that the proposed model has the upper hand against the competitors.