Abstract: In this paper, a new family of F-Loss distributions known as cosine F-Loss is proposed. This is an extension of the F-Loss family of distributions by appropriate use of trigonometric functions. The proposed method ensures that no additional parameter(s) is/are introduced in the bit to make the F-Loss family of distributions flexible. The mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Three special distributions are proposed; cosine Weibull loss, cosine Burr III loss and cosine Lomax loss. The densities exhibit different kinds of right-skewed, decreasing, reversed-J, and approximately symmetric shapes. The hazard rate functions show different kinds of increasing, decreasing, increasing-constant-increasing, increasing-constant-decreasing, reversed-J, and upside down bathtub shapes. Monte Carlo simulations are carried out to assess the behavior of the estimators. It is realized that the estimators are consistent. The applications of the proposed distributions are presented with insurance loss datasets. The results show that the cosine Burr III loss distribution provides the best parametric fit for both the business interruption claims and the automobile bodily injury claims datasets compared to the other classical heavy-tailed distributions considered.
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Keywords and phrases: trigonometric distributions, Monte Carlo simulation, heavy-tailed distributions, insurance loss, maximum likelihood estimation, F-Loss.
Received: February 4, 2023; Accepted: April 14, 2023; Published: April 22, 2023
How to cite this article: John Abonongo, Ivivi J. Mwaniki and Jane A. Aduda, A new family of F-Loss distributions: properties and applications, Advances and Applications in Statistics 87(1) (2023), 81-117. http://dx.doi.org/10.17654/0972361723030
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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