Sample Mean for Interval-valued Data

Calculate the sample barycenter of an intData object.

Usage

int_mean(data)

Arguments

data: An intData object containing the macrodata/interval data.

Value

An intData object representing the sample barycenter of the interval-valued data.

Details

Let $\boldsymbol{x}_1,\dots,\boldsymbol{x}_n$ be interval-valued observations, the sample barycenter is defined as:

$$\underset{\boldsymbol{x}}{\mathrm{arg\,min}} \sum_{h=1}^{n}{\frac{1}{n}d_\mathrm{M}^2(\boldsymbol{x}_h,\boldsymbol{x})},$$

where $d_\mathrm{M}^2()$ is the squared Mallows distance (see Mallows_dist).

This function calculates the barycenter of an intData object, which is the hyperrectangle whose center and range are the expected values of the centers ($\boldsymbol{\mu}_C$) and ranges ($\boldsymbol{\mu}_R$), respectively:

$$\boldsymbol{\mu}_B = \left(\boldsymbol{\mu}_C,\boldsymbol{\mu}_R\right),$$

with the same LatentParam, LatentCase, and LatentDist as the original intData object.

References

A. Irpino and R. Verde. Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2):143–175, Jun 2015. ISSN 1862-5355. doi:10.1007/s11634-014-0176-4

Oliveira, M. R., Pinheiro, D., & Oliveira, L. (2025). Location and association measures for interval-valued data based on Mallows' distance. arXiv preprint arXiv:2407.05105. https://arxiv.org/abs/2407.05105

Examples

data(creditcard)
credit_card_mean <- int_mean(creditcard$intData)