Distance between Distributions Group

Distance between Distributions Group of functions defined on Loss and Gain includes the following functions:

 

Full Name

Brief Name

Short Description

Kolmogorov-Smirnov Distance between Two Distributions

ksm_max

Kolmogorov-Smirnov distance between  a discrete distribution with variable probabilities of atoms and a fixed discrete distribution (as function of variable probabilities). This distance is calculated by maximizing deference between two distributions.

Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions

ksm_max_ni

Kolmogorov-Smirnov distance between a mixture of normal distributions with variable coefficients and a fixed discrete distribution  (as function of variable coefficients). This distance is calculated by maximizing deference between two distributions.

CVaR Kolmogorov-Smirnov Distance between Two Distributions

ksm_CVaR

CVaR Kolmogorov-Smirnov distance between a discrete distribution with variable probabilities of atoms and a fixed discrete distribution  (as function of variable  probabilities). This distance is calculated by taking CVaR of absolute values of differences between two distributions at atoms of the two discrete distributions with probabilities proportional to the distances between atoms.

CVaR Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions

ksm_cvar_ni

CVaR Kolmogorov-Smirnov distance between a mixture of normal distributions with variable coefficients and a fixed discrete distribution  (as function of variable coefficients). This distance is calculated by taking CVaR of absolute values of differences between two distributions at atoms of the fixed discrete distribution.

Average Kolmogorov-Smirnov Distance between Two Distributions

ksm_avg

Kantorovich  (or Average Kolmogorov-Smirnov) distance  between a discrete distribution with variable probabilities of atoms and a fixed discrete distribution. This distance is calculated by taking the average of absolute values of differences between two distributions at atoms of the two discrete distributions with probabilities proportional to the distances between atoms.

Relative Entropy

entropyr

Relative entropy where probabilities are variables

 

Remarks

1.Functions from the Distance between Distributions Group are calculated with double precision.
2.Any function from this group may be called by its "brief name" or by "brief name" with "optional name"
•The optional name of any function from this group may contain up to 128 symbols.
•Optional names of these functions may include only alphabetic characters, numbers, and the underscore sign, "_".
•Optional names of these functions are "insensitive" to the case, i.e. there is no difference between low case and upper case in these names.

 

© 2006-2016 American Optimal Decisions, Inc.