Density Estimation and Efficiency Analysis of a New Beta Polynomial Family

Abstract

A popular non-parametric approach constantly employed in the estimation of probability density function (PDF) of data is kernel density estimation (KDE) and the technique is vital in several statistical methodologies because of its functionality in data analysis. This study assesses the efficacy and efficiency of new kernel family known as the new beta polynomial family (NBPF) kernels which is generated by additional power to the polynomial functional form. The numerical efficiency of the newly introduced kernel family improves substantially due to the integration of the functional modification. The efficiencies of the classical polynomial family decreases with increase in the polynomial power while the reverse is the case with the new family which demonstrates an exceptional improvement with increase in its power and also sustaining computational flexibility. A comparative assessment of the efficiencies of NBPF shows that it exhibits superiority over the existing beta kernel family (BKF), demonstrating their adaptability to modern techniques in probability density functions without rigid parametric assumptions. Again, a real data application of the NBPF reveals that the family possesses retention capacity of intrinsic characteristics of the dataset. The numerical improvement of the efficiencies of NBPF as well as the ability of NBPF to retain essentials statistical characteristics emphasise the importance of the NBPF in data analysis and data visualization.