🤖 AI Summary
This study addresses the inadequacy of the standard binomial distribution in effectively modeling extreme values commonly observed in real-world discrete data. To overcome this limitation, the authors propose a novel heavy-tailed binomial-like distribution constructed via a weighted arithmetic average of the conventional binomial distribution and a newly devised double-uniform distribution. The resulting model retains structural simplicity while substantially enhancing tail probability representation. The paper comprehensively derives the distribution’s statistical properties, develops corresponding methods for parameter estimation and hypothesis testing, and demonstrates its superior fit and practical applicability on benchmark datasets featuring heavy-tailed discrete observations. This work exemplifies a complete statistical modeling paradigm, spanning theoretical formulation to empirical validation.
📝 Abstract
A simple alternative to the binomial distribution that places more probability weight on the tails is considered. Its derivation only requires the weighted arithmetic mean of two discrete probability mass functions, one being the binomial itself and the other being the bi-uniform introduced here. Some properties are derived, and an application to a classical data set is discussed. The presentation can be seen as an exemplary treatise on how to construct a statistical model, derive statistical properties, fit models to actual data by employing estimation methods, and verify appropriateness by using elements from statistical hypothesis testing.