Using the wrapped distribution to estimate the survival function With practical application

Abstract

This research came to present a study on the proposed wrapped-Mirra distribution as a new circular distribution that links the linear random variable and the circular variables that fall within the interval (0, 2π). The statistical and structural properties of the proposed distribution were found, such as the probability and cumulative density function, the survival function, the risk, the circular arithmetic mean, the skewness coefficient, and the kurtosis. Then, the parameters of the new distribution were estimated based on the usual maximum likelihood method (ML) and the Cramer von Mises method (CVM). For the purpose of comparing the methods of estimating the parameters of the proposed distribution, the Monte Carlo simulation method was employed to conduct several experiments with different sample sizes (25, 50, 100, 75) based on the statistical criterion mean square error (MSE). The results showed the superiority of the Cramer von Mises method (CVM) in calculating the parameters and survival function estimates for the wrapped-Mirra distribution in general in estimating the distribution parameters sizes. The distribution was applied to real data of (100) observations representing the femoro-tibial angles (FTA) of people suffering from bow legs disease in Karbala Governorate by applying this data to the proposed distribution using the Cramer von Mises method (CVM), which appeared to be superior in the experimental aspect among the estimation methods used.