Abstract
In this paper, a new three-parameter power inverted Nadarajah–Haghighi distribution is proposed and studied. The new distribution is a generalization of the inverted Nadarajah–Haghighi distribution in which an additional shape parameter is included. Surprisingly, this additional shape parameter dominates the tails’ weights of distribution and also affects skewness and kurtosis. Such heavy-tailed distributions are suitable for fitting actuarial and financial risk real problems. Important mathematical properties of this distribution are obtained. Characterization based on two truncated moments is also derived. The parameters are estimated using the maximum likelihood method. Further, a numerical simulation study is conducted for reinforcement of the results. Finally, the application of the proposed distribution to real-life data sets is presented to prove its applicability.