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# A Cantelli-Type Inequality for Constructing Non-Parametric P-Boxes Based on Exchangeability

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications*, PMLR 103:386-393, 2019.

#### Abstract

In this paper we prove a new probability inequality that can be used to construct p-boxes in a non-parametric fashion, using the sample mean and sample standard deviation instead of the true mean and true standard deviation. The inequality relies only on exchangeability and boundedness.