Ranking Forecasts by Stochastic Error Distance, Information, and Reliability Measures

Maximum entropy distributions with quantile information

“…Specific models provided elaborations of the uniform, exponential, normal, Laplace, and a known asymmetric Laplace distribution. The elaboration of the Laplace distribution is along the lines of Ardakani, Ebrahimi, and Soofi (2018) that explored the link between the information theory and Laplace’s first and second laws of error in terms of the minimum risk ME models under the absolute error and quadratic loss functions (Laplace and normal). This extension provides a gateway to further research on developing ME models with minimum risks of other asymmetric loss functions such as Linex loss which is used in various problems.…”

Assessing point forecast accuracy by stochastic error distance

“…Another direction is further study of M AE vs. M SE rankings as introduced in section 3. In work building on the research reported here, Ardakani et al (2015) take interesting steps in that direction, obtaining analytic results under a "convex ordering" assumption weaker than a normality. Necessary and sufficient conditions remain elusive, however, for the general case of non-Gaussian, non-zero-mean forecast errors.…”

On reconsidering entropies and divergences and their cumulative counterparts: Csiszár's, DPD's and Fisher's type cumulative and survival measures

“…It is clear that if the random quantities and , associated with and , are non-negative, then and are equal to and , respectively. It should be mentioned at this point that Asadi et al [2] defined, in Subsection 3.2, a Kullback–Leibler type divergence function between two non-negative functions and which provides a unified representation of the measures (6), (23) and (24), with , being probability density function, cumulative distribution function and survival function, respectively. Based on Asadi et al [7], for non-negative random variables and , associated with and , respectively, and (23), (24) are simplified as follows, and …”