On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications

A new two-parameter model is proposed using the Kavya–Manoharan (KM) transformation family and Burr X (BX) distribution. The new model is called the Kavya–Manoharan–Burr X (KMBX) model. The statistical properties are obtained, involving the quantile (QU) function, moment (MOs), incomplete MOs, conditional MOs, MO-generating function, and entropy. Based on simple random sampling (SiRS) and ranked set sampling (RaSS), the model parameters are estimated via the maximum likelihood (MLL) method. A simulation experiment is used to compare these estimators based on the bias (BI), mean square error (MSER), and efficiency. The estimates conducted using RaSS tend to be more efficient than the estimates based on SiRS. The importance and applicability of the KMBX model are demonstrated using three different data sets. Some of the useful actuarial risk measures, such as the value at risk and conditional value at risk, are discussed.