Beta exponential Teissier distribution: properties and parameters estimation under ranked set sampling

This paper introduces a novel four-parameter distribution, referred to as beta exponential Teissier distribution. This distribution includes the Teissier, beta Teissier, exponentiated Teissier, and exponential generalized Teissier distributions as special cases. Its important mathematical properties are derived, including expansions for the cumulative distribution and density functions, quantile function, moments, moment generating function, incomplete moments, entropies, order statistics and their moments, as well as stress strength reliability. Using a simple random sampling and ranked set sampling based on the perfect ranking assumption, the maximum likelihood estimation of the model’s parameters is determined. A simulation study is provided to evaluate the performance of the estimates using the two sampling schemes. Additionally, the relative efficiencies and asymptotic confidence intervals are calculated. To showcase the practical application, three data sets were examined using the proposed model, validating its applicability. This study opens a new avenue for the application of the beta exponential Teissier distribution in environmental and health-related applications.