A method to assess the accuracy of pseudo-random number sampling methods from evacuation datasets

Abstract

We propose a method for assessing the accuracy of pseudo-random number sampling methods for evacuation modelling purposes. It consists of a systematic comparison between experimental and generated distributions. The calculated weighted relative error (Ew_rel) is based on the statistical parameters as central moments (mean, standard deviation, skewness and kurtosis) to shape the distribution. The case study involves the Box?Muller transform, the Kernel-Epanechnikov, the Kernel-Gaussian and the Piecewise linear generating samples from eight evacuation datasets fitted against normal, lognormal and uniform distributions. Keeping in mind that the Bos Muller method has two potential sources of error (i.e. distribution fitting and sampling), this method produces plausible results when generating samples from the three types of distributions (Ew_rel<0.30 for normal, lognormal and uniform distributions). We also fund that the Kernel Gaussian and the Kernel Epanechnikov methods are well accurate in generating samples from normal distributions (Ew_rel<0.1) but potentially inaccurate when generating samples from uniform and lognormal distributions (Ew_rel > 0.80). Results suggest that the Piecewise linear is the most accurate method (Ew_rel = 0.01 normal; Ew_rel = 0.04 lognormal; Ew_rel = 0.009 uniform). This method has the advantage of sampling directly from empirical datasets i.e. no previous distribution fitting is needed. While the proposed method is used here for evacuation modelling, it can be extended to other fire safety engineering applications.