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Theory and Finite-Sample Inference for a Novel Circular Probability Distribution in Directional Statistics |
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PP: 1733-1756 |
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doi:10.18576/amis/200617
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Author(s) |
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Mohamed S. Eliwa,
Hend S. Shahen,
Mahmoud El-Morshedy,
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Abstract |
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| In this paper, we offer a new circular probability model with a single parameter by translating a one-parameter linear- exponential distribution on a circle of [0,2π). The resulting model, referred to as the wrapped one-parameter linear-exponential (WrOPLE) distribution, has closed form expressions for both probability density and cumulative distribution functions, which enable an analytically tractable examination of crucial probabilistic and directional features. Explicit formulas are derived for the wrapped and unwrapped characteristic functions, trigonometric moments, mean direction, mean resultant length, circular variance, circular standard deviation and measurements of circular skewness and kurtosis. The features of reliability theory are explored, including the hazard rate function, reversed hazard rate function, mean residual life and mean inactivity time and their boundary properties. We explore the geometrical and asymptotic aspects of the model by means of the density-shape, the limiting behavior and modality. There are well known requirements for the shift of the density from an internal unimodal configuration to a boundary mode. In this study, the method of maximum likelihood estimation of the unknown parameter is established and a Monte Carlo simulation analysis of the finite sample performance is undertaken for different parameter settings and sizes of the sample exhibiting greater estimate accuracy in larger sample size. We evaluate our methods on real directed data sets and compare to known wrapped distributions via probability based metrics, circular summary statistics and visual examination. The WrOPLE distribution provides a flexible and analytically tractable extension of the wrapped model family for the directional sustainability data considered, delivering competitive performance within a parsimonious one-parameter framework. |
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