Abstract
There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.
Highlights
Directional statistics is an emerging area of statistics and is being used as a tool for practitioners in many scientific fields such as astronomy, biology, earth science, meteorology, medicine and physics
One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach
We study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix
Summary
Directional statistics is an emerging area of statistics and is being used as a tool for practitioners in many scientific fields such as astronomy, biology, earth science, meteorology, medicine and physics. The directions may be regarded as points on the circumference of a circle (in two dimensions) or on the surface of a sphere (in three dimensions). For discrete circular models, Girija et al (2014) derived characteristics functions of the wrapped Poisson distribution. Brobbey et al (2016) introduced a new discrete circular distribution, the wrapped zeroinflated Poisson (WZIP) distribution and derived its population characteristics. We study the estimation of the parameters of the WZIP and WP distributions using estimating functions, and derive asymptotic distribution of the tangent of the mean direction. We first briefly discuss the wrapped discrete distribution and WZIP distribution as given in Brobbey et al (2016)
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