Probability Distribution Modeling of Scanner Prices and Relative Prices

Abstract

The article deals with the problem of the proper selection of the theoretical distribution to describe the empirical distribution of scanner prices. In the empirical study we use scanner data from one retail chain in Poland, i.e. monthly data on natural yoghurt, drinking yoghurt, long grain rice and coffee powder sold in 212 outlets in January and February 2022. Prices and price relatives were modeled using selected ten probability distributions with non-negative support, including two, three and four-parameter family of distributions In addition to the visual assessment in the form of empirical PDF and CDF figures, numerical criteria were used. These include information criteria values such as AIC, BIC, HQIC and p values calculated for the K-S, AD and CVM goodness-of-fit tests. Our research showed that at least two models could be distinguished as very accurate, which provides a good background for simulation research on price indices or for the construction of so-called population price indices.