mean-methods: Calculate the sample Aumann mean of a random interval

In IntervalQuestionStat: Tools to Deal with Interval-Valued Responses in Questionnaires

Calculate the sample Aumann mean of a random interval

Description

This function calculates the sample Aumann mean of a single realization formed by n nonempty compact real intervals drawn from a random interval saved as an IntervalList object.

Usage

## S4 method for signature 'IntervalList'
mean(x)

Arguments

x	A list of intervals, that is, an IntervalList object.

Details

Let \mathcal{X} be an interval-valued random set and let ≤ft(x_{1},x_{2},…,x_{n}\right) be a sample of n independent observations drawn from \mathcal{X}. Then, the sample Aumann mean (see Aumann, 1965) is defined as the following interval given by

\overline{x} = \frac{1}{n}∑_{i=1}^{n} x_{i}.

Value

This function returns an IntervalData object with the calculated sample Aumann mean of the given n intervals, which is defined as another nonempty compact real interval.

Author(s)

José García-García [e-mail]

References

Aumann, R.J. (1965). Integrals of set-valued functions. Journal of Mathematical Analysis and Applications, 12(1):1-12. doi: 10.1016/0022-247X(65)90049-1.

See Also

Other sample dispersion and covariance measures such as sample Fréchet variance and sample covariance can be calculated through var() and cov() functions, respectively.

Examples

## Some mean() trivial examples
list <- IntervalList(c(1, 3), c(2, 5))
mean(list)

IntervalQuestionStat documentation built on Nov. 1, 2022, 5:06 p.m.