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Rp-Parameters Estimation of a Half Circular Inverse Gamma distribution with an application.pdf

In many practical applications and in the reality of our lives, we may encounter data measured in angular units such as degrees or radians, and this data can fall within the full circular range, i.e. (0, 2π) and such data is called the circular data, as the supporter Support for circular data is the unit circle while for linear data the support is the real number line R, The term circular data is used for the purpose of distinguishing it from linear data that is often used in analytics, or it may lie in the half-circular range (0, π), as this type of data is called half-circular data. In the case of half-circular data Circular, A model should be found for the purpose of studying and analyzing such data. Therefore, this thesis came to find the semi-circular inverse gamma distribution based on the inverse stereographic projection property, which is concerned with converting the normal (Cartesian) data into polar data (measured by angles) and then finding the characteristics of the new semi-circular distribution, And then estimating the parameters of the new distribution based on three methods of estimation, namely the method of the maximum likelihood (Maximum Likelihood), the method of the least Hellinger distance with one step (The One-Step Minimum Hellinger Distance Estimator) and the method of general distance (The General spacing estimator) and then applying The estimations extracted on real data and using simulation experiments were compared between the three methods and we concluded that the best method for estimating the parameters of the semicircular inverted gamma distribution is the one-step Hellinger least distance method (OHD) with a better percentage (50%), followed by the greatest possibility method (MLE). ) with a preference rate of (35%), and finally the general distance method (GS) with a preference rate of (15%). As well as the use of real data (data of angles of curvature of the cornea back) using a retinal scanner OCT device for three-dimensional tomography, in which pictures were taken of the back of the eyes of (100) patients. The variable that represents the studied data is the angle measured in radians, which measures the posterior curvature of the cornea, and it was found that the real data fit the distribution of the transformed semicircular inverse gamma.