Probability Distribution Modelling of Scanner Prices and Relative Prices Using Theoretical Distributions with Two, Three, Four, and Five Parameters

Abstract

This article addresses the problem of proper adjustment of the theoretical probability distribution to 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 yogurt, yogurt drinks, long grain rice and coffee powder sold in 212 outlets in January and February 2022. Prices and relative prices are modelled using fifty two‑, three‑, four‑, and five‑parameter probability distributions with non‑negative support. Some of them consist of somewhat known distributions which are called their special cases. The study indirectly involves over a hundred of these distributions. Information criteria such as AIC, BIC, HQIC and p‑values of goodness‑of‑fit tests are used for comparative analysis. This article shows that models such as Frechet, Pareto IV  and Log‑Logistic could be distinguished as very accurate, which provides a good background for simulation research on price indices or for the construction of the so‑called population price indices. The Appendix presents the cumulative distribution function formulas of the models used and the necessary R codes for conducting the research.