| mean {IntervalQuestionStat} | R Documentation |
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 |
Details
Let \mathcal{X} be an interval-valued random set
and let \left(x_{1},x_{2},\ldots,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}\sum_{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 garciagarjose@uniovi.es
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)