Exponentiated Arctan-X Family of Distribution: Properties, Simulation and Applications to Insurance Data
Keywords:
Percentage points, maximum likelihood estimation method, Fisher’s inverse matrix, confidence intervalAbstract
A new family of distribution has been investigated in this paper. Exponentiated method has been used to generate the new family of distribution. The proposed family of distribution is known as the exponentiated arctan-X family of distributions which are immensely beneficial and play an important role in modelling data sets. Various properties like reliability analysis, moments, moment generating function, quantile function, median are studied. Exponential distribution has been taken as a special case for the specific purpose of the show of strength. To estimate the parameters of the exponentiated arctan exponential distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. A complete percentage point study has been discussed and presented. The exponentiated arctan exponential model is demonstrated using two life-time data sets. The proposed family of distribution is compared to well-known two, three, and four parameter competitors. For model comparison, we used the most precise tests used to know whether the exponentiated arctan-exponential distribution is more useful than competing models.
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