Application of Choquet Calculus to Statistics With Distorted Probabilities

This paper deals with distorted statistics as statistics based on distorted probabilities by applying Choquet calculus. First, elementary distorted statistics on the nonnegative line is explored for exponential and Gaussian distributions. Next, by introducing Choquet calculus for real-valued functions on the real line, distorted statistics is explored for uniform and normal distributions. Finally, the relations of distorted statistics with conventional skew statistics are clarified.