Discover how tail risk impacts portfolios, why rare financial events matter, and strategies for safeguarding investments against significant, unexpected losses.

This document archives a sophisticated system of **applied, embodied mathematics** developed by Southern African foraging communities—including the San, Zulu, Xhosa, Venda, Tsonga, Hadza, and BaAka.

Interest Rate Probability Distributions Implied by Derivatives Prices is a daily measure of the distribution of future short-term interest rates, calculated from prices of fixed-income derivatives ...

In rural areas, continuous changes require managers to seek technologies to improve the property’s sustainability. Thus, the present research aimed to develop a constructivist multi-criteria model for ...

Introduction: Caffeine, a central nervous system stimulant, with 80% worldwide consumption. Despite its popularity, limited research has evaluated caffeine exposure in Saudi Arabia (SA). Given that ...

ABSTRACT: Singh, Gewali, and Khatiwada proposed a skewness measure for probability distributions called Area Skewness (AS), which has desirable properties but has not been widely applied in practice.

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...

Abstract: The manuscript introduces the mathematical representation of the neutrosophic triangular distribution, encompassing probability density functions and cumulative distribution functions. Two ...