Efficient entropy estimation for inverted exponentiated Pareto distribution using ranked set sampling: A comparative study

Entropy, a key concept in information theory, measures the degree of unpredictability or uncertainty present in a random variable or system. It plays a vital role across various disciplines, including communication theory, thermodynamics, and statistical mechanics. On the other hand, Ranked Set Sampling (RSS) provides an effective approach to mitigating the challenges associated with costly or complex measurement procedures. Given the wide-ranging applications of the inverted exponentiated Pareto distribution, this study investigates the estimation of its parameters and various entropy measures, encompassing Havrda and Charvát, Tsallis, Rényi, and Arimoto. We examine the performance of these estimators under both RSS and simple random sampling (SRS) frameworks.To tackle this task, seven classical estimation techniques are employed: maximum product spacing, least squares, Kolmogorov, Anderson-Darling, weighted least squares, maximum likelihood, and Cramér-von Mises. Using an equal number of measured units, simulation studies evaluates the performance of estimators derived from SRS and RSS, considering both perfect and imperfect ranking scenarios. Three evaluation criteria are adopted for comparison: relative efficiency, mean squared error, and absolute bias. In assessing the estimated quality of RSS and SRS, the Kolmogorov technique appears beneficial in most cases, based on numerical results. In terms of estimation accuracy, RSS consistently performs better than SRS, regardless of whether the ranking is perfect or imperfect. Additionally, compared to imperfect ranking method, perfect ranking produces estimates that are more accurate. The advantage of the RSS design over the SRS design is further supported by real data results that indicate the tensile strength measures in GPA carbon fibers.