distance-methods: Calculate the theta-distance between two intervals

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

Calculate the θ-distance between two intervals

Description

This function calculates the θ-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 θ-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_{θ}(A,B) = √{(\mathrm{mid}~A - \mathrm{mid}~B)^2 + θ\cdot(\mathrm{spr}~A -\mathrm{spr}~B)^2},

where θ is a positive real number.

Value

This function returns the calculated θ-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

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