WassSqDistH {HistDAWass}

Method WassSqDistH

Description

Computes the squared L2 Wasserstein distance between two distributionH objects.

Usage

WassSqDistH(object1, object2, ...)

## S4 method for signature 'distributionH,distributionH'
WassSqDistH(object1 = object1, object2 = object2, details = FALSE)

Arguments

object1

is an object of distributionH class

object2

is an object of distributionH class

...

optional parameters

details

(optional, default=FALSE) is a logical value, if TRUE returns the decomposition of the distance

Value

If details=FALSE, the function returns the squared L2 Wasserstein distance.
If details=TRUE, the function returns list containing the squared distance, its decomposition in three parts (position, size and shape) and the correlation coefficient between the quantile functions.

References

Irpino, A. and Romano, E. (2007): Optimal histogram representation of large data sets: Fisher vs piecewise linear approximations. RNTI E-9, 99-110.
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

## ---- create two distributionH objects ----
mydist1 <- distributionH(x = c(1, 2, 3), p = c(0, 0.4, 1))
mydist2 <- distributionH(x = c(7, 8, 10, 15), p = c(0, 0.2, 0.7, 1))
# -- compute the squared L2 Waaserstein distance
WassSqDistH(mydist1, mydist2)
# -- compute the squared L2 Waaserstein distance with details
WassSqDistH(mydist1, mydist2, details = TRUE)