distance {IntervalQuestionStat}

Calculate the \theta-distance between two intervals

Description

This function calculates the \theta-distance between any two nonempty compact real intervals.

Usage

## S4 method for signature 'IntervalData,IntervalData'
distance(e1, e2, theta = 1)

Arguments

e1

A single interval stored as an IntervalData object.

e2

A single interval stored as an IntervalData object.

theta

A single positive real number stored as a unique numeric value which is used for distance computations. By default, theta = 1.

Details

The \theta-distance between any two given nonempty compact real intervals, A and B, was defined by Gil et al. (2002) as the non-negative real number calculated as follows,

d_{\theta}(A,B) = \sqrt{(\mathrm{mid}~A - \mathrm{mid}~B)^2 + \theta\cdot(\mathrm{spr}~A -\mathrm{spr}~B)^2},

where \theta is a positive real number.

Value

This function returns the calculated \theta-distance between the two given intervals, which is defined as a single real number. Therefore, the output of this function is a single numeric value.

Author(s)

José García-García [e-mail]

References

Gil, M.Á.; Lubiano, M.A.; Montenegro, M.; López, M.T. (2002). Least squares fitting of an affine function and strength of association for interval-valued data. Metrika, 56:97-111. doi:10.1007/s001840100160.

Examples

## Some distance() examples
i1 <- IntervalData(0, 1)
i2 <- IntervalData(3, 7)
distance(i1, i2)      ## rho2 distance
distance(i1, i2, 1/3) ## Bertoluzza's distance with Lebesgue measure