On composite length-biased exponential-Pareto distribution: Properties, simulation, and application in actuarial science

The composite length-biased exponential-Pareto (CLBEP) distribution is a new composite distribution that is introduced in this article. This model's probability density function, moments, and quantiles, among other statistical characteristics, are determined mathematically. The parameters' maximum-likelihood estimation and stochastic ordering are discussed. A comparison study with other new composite and conventional distributions is also included. Specifically, using two actual fire insurance data sets, the goodness of fit of this new model is contrasted with the composite exponential-Pareto, composite lognormal-Pareto, and composite Rayleigh-Pareto distributions (Algerian and Danish fire insurance losses). 2010 AMS subject classifications 62E10; 60E05.