On the distribution of the product of two continuous random variables with an application to electricity market transactions. Finite and infinite-variance case

TL;DR

This paper derives formulas for the distribution of the product of two continuous random variables, including Gaussian, log-normal, Student's t, and Pareto, with applications to electricity market transaction data.

Contribution

It provides new formulas for the distribution and moments of products of various random variables, considering both independent and correlated cases.

Findings

Derived explicit formulas for PDFs and moments of product distributions.

Applied maximum likelihood estimation to real electricity market data.

Analyzed transaction value distribution as a product of prices and volumes.

Abstract

In this paper we study the distribution of a product of two continuous random variables. We derive formulas for the probability density functions and moments of the products of the Gaussian, log-normal, Student's t and Pareto random variables. In all cases we analyze separately independent as well as correlated random variables. Based on the theoretical results we use the general maximum likelihood approach for the estimation of the parameters of the product random variables and apply the methodology for a real data case study. We analyze a distribution of the transaction values, being a product of prices and volumes, from a continuous trade on the German intraday electricity market.