dotpW {HistDAWass}

Method dotpW

Description

The dot product of two distributions inducing the L2 Wasserstein metric

The dot product of a number (considered as an impulse distribution function) and a distribution

The dot product of a distribution and a number (considered as an impulse distribution function).

Usage

dotpW(e1, e2)

## S4 method for signature 'distributionH,distributionH'
dotpW(e1, e2)

## S4 method for signature 'numeric,distributionH'
dotpW(e1, e2)

## S4 method for signature 'distributionH,numeric'
dotpW(e1, e2)

Arguments

e1

a distributionH object or a number

e2

a distributionH object or a number

Value

A numeric value

Author(s)

Antonio Irpino

References

Irpino, A., Verde, R. (2015) Basic statistics for distributional symbolic variables: a new metric-based approach Advances in Data Analysis and Classification, DOI 10.1007/s11634-014-0176-4

Examples

## let's define two distributionH objects
mydist1 <- distributionH(x = c(1, 2, 3, 10), p = c(0, 0.1, 0.5, 1))
mydist2 <- distributionH(x = c(5, 7, 15), p = c(0, 0.7, 1))

## the dot product between the distributions
dotpW(mydist1, mydist2) #---> 39.51429

## the dot product between a distribution and a numeric
dotpW(mydist1, 3) #---> 13.2
dotpW(3, mydist1) #---> 13.2


# DOTPW method -----