# WassSqDistH-methods: Method 'WassSqDistH' In HistDAWass: Histogram-Valued Data Analysis

## Description

Method `WassSqDistH`

Computes the squared L2 Wasserstein distance between two `distributionH` objects.

## Usage

 ```1 2 3 4 5``` ```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

 ```1 2 3 4 5 6 7``` ```##---- 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) ```

HistDAWass documentation built on Dec. 7, 2017, 5:03 p.m.