Properties and applications of the Tan Weibull loss distribution

Probability models play crucial role in modeling loss in the finance and actuarial sciences. In this article, a new family of loss distributions known as the Tan F-Loss family of distributions is proposed with the Tan Weibull Loss distribution as a special case. The density exhibits decreasing, right skewed, symmetric, and approximately symmetric shapes. The hazard rate function shows decreasing and modified bathtub shapes. The statistical properties of the Tan Weibull Loss distribution including the quantile function, moments, expansion of the general rate, moment generating function, incomplete moment, and order statistics are studied. The maximum likelihood estimators of the distribution are also studied. Simulations are carried out to examine the behavior of the estimators. The results show that the estimators are consistent. The usefulness of the proposed distribution is demonstrated with two insurance loss datasets. The results show that the proposed distribution gives a better parametric to the two datasets compared with the competing distributions.