The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

A family of integrals over infinite intervals appears frequently in the statistical literature on non-parametric regression. This note presents two simple transform methods, based on beta function and Parseval identity, to explicitly evaluate these integrals. These methods will benefit researchers and practitioners working in non-parametric…