Statistical Estimation Using some Kernel Functions

Abstract

In this article aims to provide accurate statistical estimation of the probability density function (PDF) for survival data using selected asymmetric kernel functions ) Lindley, Gamma1, Weibull, Inverse-Gaussian) ). The focus was on developing a flexible model employing the Weibull function as an asymmetric kernel, given its suitability for positive and skewed data. In the theoretical part, the proposed kernel function was defined, its properties analyzed, and it was theoretically compared with existing kernels in terms of form, probabilistic behavior, and representational capability.

In the experimental part, a simulation study was conducted across three different sample sizes and data scenarios to assess the performance of the proposed kernel against other symmetric and asymmetric kernels, based on the Integrated Squared Error (ISE) criterion, using both Silverman’s rule and Cross-Validation for bandwidth selection. The results showed the superiority of the Weibull kernel, particularly for a sample size of 200, where it achieved the lowest ISE values.

The model was further applied to real-world survival data from catheter patients in a general hospital. The analysis demonstrated the efficiency of the proposed model through the close agreement between the estimated and actual survival functions, evaluated via AIC and p-value metrics. This study highlights the effectiveness of asymmetric kernels especially the Weibull kernel in accurately modeling positive skewed data.