Efficient Parameter Estimation for the Inverse Power Moment Exponential Model under Ranked Set and Simple Random Sampling with Entropy Measures and Applications

Abstract

It is challenging to model real-world data with complex features, such as skewness, heavy tails, and high variability, because each one demands a distinct probability density function. For these kinds of data, a variety of statistical models can be applied; the right data type should be chosen. When working with units in a population is costly, the ranked set sampling (RSS) technique is crucial for obtaining data. Nevertheless, they can be easily categorized by the relevant variable. Moreover, entropy information quantifies how unpredictable or uncertain a random variable or mechanism is. It is essential to many different fields, notably reliability engineering, environmental studies, medical sciences, economics, actuarial science, finance, and insurance. In this study, we applied the inverse power moment exponential (IPME) model to estimate model parameters from RSS and simple random sampling (SRS) designs using various estimation methods. We additionally introduced several entropy measures, including Rényi, Shanon, Havrda and Charvat, Tsalis, Arimoto, and Mathai-Haubold entropies for the IPME model. A thorough simulation investigation is performed to verify the effectiveness of the proposed estimators under RSS and SRS schemes by calculating the mean, mean squared error, and relative efficiency. The use of real-world datasets further emphasizes the proposed RSS design compared with the SRS scheme. Overall, the findings highlight the potential of the RSS technique as a robust and flexible tool for estimating the model parameters and for obtaining data sets.