Estimating Probability Density Function of Vehicle-Related Time Series Data using Histogram Cubic B-Spline Approximation

Abstract: Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed distribution governing the random process under examination. Diverse methodologies exist for estimating PDFs, each offering distinct advantages in specific contexts. This publication presents a novel approach that centers on estimating probability density functions by leveraging histograms and B-spline curves, with a particular focus on analyzing vehicle-related time series data. The proposed method outlines a comprehensive framework for estimating PDFs tailored specifically to the study of vehicle-related phenomena. By effectively combining the strengths of histograms and B-spline curves, researchers gain a powerful toolset to obtain precise and reliable estimations of PDFs, thereby enabling advanced analysis and comprehension of vehicle-related random processes in scientific investigations.