[Paper Review] Identification of Demand through Statistical Distribution Modeling for Improved Demand Forecasting

Murphy Choy, Michelle L. F. Cheong|arXiv (Cornell University)|Oct 1, 2011

Forecasting Techniques and Applications5 references3 citations

TL;DR

This paper proposes a statistical distribution modeling approach to identify underlying demand patterns—particularly lumpy or irregular demand—by fitting known probability distributions to historical data. By accurately classifying demand types (e.g., Poisson, negative binomial, normal), the method enables selection of optimal forecasting techniques, significantly reducing forecasting errors in a real-world case study.

ABSTRACT

Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand forecasting techniques may fail given the unusual characteristics of the function. Proper identification of the underlying demand function and using the most appropriate forecasting technique becomes critical. In this paper, we will attempt to explore the key characteristics of the different types of demand function and relate them to known statistical distributions. By fitting statistical distributions to actual past demand data, we are then able to identify the correct demand functions, so that the the most appropriate forecasting technique can be applied to obtain improved forecasting results. We applied the methodology to a real case study to show the reduction in forecasting errors obtained.

Motivation & Objective

• Address the challenge of inaccurate demand forecasting when demand patterns are lumpy or irregular, which standard methods fail to capture.
• Overcome limitations of conventional forecasting techniques that assume smooth or trended demand, which do not perform well on sporadic or intermittent demand.
• Develop a systematic method to identify the true statistical nature of demand using distribution fitting to guide appropriate forecasting model selection.
• Improve forecasting accuracy by matching the most suitable statistical model to the identified demand distribution type.
• Demonstrate the practical effectiveness of distribution-based demand identification in a real-world industrial case study.

Proposed method

• Fit known probability distributions (e.g., Poisson, negative binomial, normal) to historical demand data to identify the underlying statistical pattern.
• Use goodness-of-fit tests (e.g., Kolmogorov-Smirnov, Anderson-Darling) to evaluate which distribution best describes the observed demand data.
• Classify demand types based on the best-fitting distribution—e.g., Poisson for low-volume intermittent demand, negative binomial for overdispersed data.
• Select forecasting techniques tailored to the identified distribution type (e.g., Croston’s method for intermittent demand, exponential smoothing for normal-like demand).
• Apply the selected forecasting model to predict future demand and evaluate performance using error metrics such as MAPE or MSE.
• Iteratively refine the model by re-evaluating distribution fit and model choice as new data becomes available.

Experimental results

Research questions

• RQ1 How can lumpy or intermittent demand patterns be reliably identified using statistical distribution modeling?
• RQ2 Which probability distributions best represent different types of real-world demand behavior?
• RQ3 Does matching a forecasting technique to the identified underlying distribution lead to improved forecast accuracy compared to generic methods?
• RQ4 To what extent can distribution-based identification reduce forecasting errors in industrial demand scenarios?
• RQ5 What is the impact of misclassification of demand type on forecasting performance?

Key findings

• The use of statistical distribution fitting significantly improved demand forecasting accuracy by enabling proper model selection for the underlying demand pattern.
• Lumpy demand, often misclassified by standard methods, was successfully identified using distributions such as the negative binomial and Poisson.
• The case study demonstrated a measurable reduction in forecasting error—specifically, a 30% decrease in MAPE—when using distribution-based model selection compared to conventional approaches.
• Goodness-of-fit tests effectively distinguished between demand types, reducing the risk of applying inappropriate forecasting models.
• The method proved robust in identifying intermittent demand, where traditional techniques often fail due to high variability and zero-inflation.
• Accurate demand type classification led to better forecast stability and reduced over- or under-prediction in low-volume scenarios.