2022/10/30 by Yunran Wei, Wei, Yunran, Ričardas Zitikis +1
Decision Sciences · Mathematics · #Applications (stat.AP) #Artificial intelligence #Computer science #Cumulative distribution function #Distribution (mathematics) #Econometrics #FOS: Computer and information sciences #FOS: Economics and business #Forecasting Techniques and Applications #Function (biology) #Inference #Mathematics #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Probability density function #Probability distribution #Quantile #Quantile function #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistical inference #Statistics
paper · pdf · doi:10.48550/arxiv.2210.16880
openalex publication_date 2022/10/30 · openalex created_date 2022/11/06 · openalex updated_date 2026/08/01
This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various perspectives. The invention helps to avoid a number of technical assumptions that have been traditionally imposed when working with quantities containing quantiles. In particular it helps to completely avoid the requirement of the existence of a probability density function. The developed results explain and illustrate the invention, whose byproducts include the assessment of model uncertainty and misspecification, and the derivation of statistical inference results.