Exact probability distribution function for the volatility of cumulative production

TL;DR

This paper derives the exact probability distribution function for the volatility of cumulative production, generalizing previous models to include arbitrary noise distributions, thereby enhancing understanding of production variability.

Contribution

It provides a mathematical framework for the volatility distribution of cumulative production under arbitrary noise, extending prior work limited to normal noise assumptions.

Findings

Generalized volatility distribution for arbitrary noise

Mathematical foundation applicable to diverse industrial processes

Facilitates future research on production and market strategies

Abstract

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on production and market strategy.