Empirical estimation of probability distribution for electric field strength in automotive cabin

Abstract

A novel model of the probability distribution for electric field strength in automotive cabin is proposed in the form of a mixture distribution of a linear Rayleigh distribution for low-value data and a log generalized extreme value (GEV) distribution for high-value data. A sample model is estimated from the data measured in a horizontal two-dimensional area above main battery in a hybrid vehicle. For the probability distribution model of the ensemble data of different transmitter antenna directions and all target frequencies, the mixture weights and the parameters for each component distribution are estimated using expectation-maximization (EM) algorithm. The result model showed good fitting to the measured data in probability density function plot and quantile-quantile (Q-Q) plot. Based on the ensemble data distribution model, the probability distribution models for individual conditions of frequencies and antenna-directions are also estimated applying linear transformation. Results are tested using Q-Q plot, which shows good fitting with slight overestimation in very high-value region. Kolmogorov-Smirnov (K-S) goodness of fit test at the 1% significance level also accepts this method for all the data measured above 600MHz.