Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications

Abstract

In this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. It can be asymmetric, such as bathtub, unimodal, increasing and decreasing. In addition, the shape forms of the hrf for the KMKu model can be bathtub, U-shaped, J-shaped and increasing. Several statistical and computational properties were computed. Four different measures of entropy were studied. The maximum likelihood approach was employed to estimate the parameters for the KMKu model under simple and ranked set sampling. A simulation experiment was conducted in order to calculate the model parameters of the KMKu model utilizing simple and ranked set sampling and show the efficiency of the ranked set sampling more than the simple random sampling. The KMKu has more flexibility than the Ku model and other well-known models, and we proved this using three real-world data sets.