Log-Normal Distribution Modelling with Quantised Data

A continuous distribution can be a helpful way to describe natural phenomena, e.g. service times of repairable systems and human tissue growth can be modelled using a log-normal distribution. When a dataset is modified by rounding or truncation, data may become distorted enough not to fit its original distribution due to the quantisation errors. Attempting to fit statistical distributions can even result in convergence errors while fitting if, for example, values are rounded to zero. We explore the effects of quantisation when distribution fitting. We provide a framework to identify impacts of quantisation and different techniques to adjust quantised data and mitigate convergence errors. We specifically look at a log-normal distribution and demonstrate that adding a relative constant based on decimal length can eradicate convergence errors and weaken quantisation.