The Marshall-Olkin Extended Circular Uniform (MOECU) Distribution: Its Properties and Application
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Abstract
Circular data arise naturally in numerous scientific fields, including meteorology, biology, geology, environmental sciences, and directional statistics. The development of flexible circular distributions capable of modeling asymmetric angular observations remains an active area of research. In this article, we introduce the Marshall-Olkin Extended Circular Uniform (MOECU) distribution, a new one-parameter circular distribution on the interval , obtained through the Marshall-Olkin transformation [1] to the circular uniform baseline distribution. The proposed model possesses a simple closed-form probability density function, cumulative distribution function, and quantile function, making it particularly attractive for theoretical investigations and practical utility. We derive the characteristic function and trigonometric moments of the distribution, and obtain its population characteristics. The hazard rate, mode and median are also examined. The parameter is estimated by the method of maximum likelihood and the finite sample performance of the estimator is investigated through an extensive Monte Carlo simulation study, together with several rival estimation techniques(least squares, weighted least squares, Cramer-Von Mises, Anderson-Darling and its variants: maximum product of spacing’s, and percentile method) The practical applicability of the MOECU distribution is illustrated using the classical angular data on orientations of starhead topminnows[2](FisherB4), where it is compared with several competing circular models through standard goodness-of-fit measures. The results demonstrate that the proposed distribution provides an effective and parsimonious alternative for modeling asymmetric circular data and yields competitive performance in practical applications.
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