A New Shifted Lomax-X Family of Distributions : Properties and Applications to Actuarial and Financial Data

Abstract

The Lomax distribution, which is often used to describe severe losses and financial risks because of its heavy tail features, is the basis distribution of the shifted Lomax (SHL-X) family of distributions that we propose in this study. The main objective is to increase the adaptability and accuracy of the traditional Lomax model in the representation of complex data sets. We explore various mathematical properties of the special member called the shifted Lomax Weibull (SHL-W), including its moments, quantile function and entropy measures. We employ the maximum likelihood estimation approach to estimate the parameters of the SHL-W distribution. Simulation studies are conducted to evaluate the estimators’ accuracy and dependability. The practical applicability of the proposed model is demonstrated by its application to insurance data, highlighting its effectiveness in modeling claims and determining appropriate premium rates.The findings highlight the new model’s potential for broader applications in risk management and financial analysis by showing that it is more data-adapted than competing models.