ordinal_dispersion_2 {otsfeatures}R Documentation

Computes the estimated dispersion of an ordinal time series according to the approach based on the diversity coefficient (DIVC)

Description

ordinal_dispersion_2 computes the estimated dispersion of an ordinal time series according to the approach based on the diversity coefficient

Usage

ordinal_dispersion_2(series, states, distance = "Block", normalize = FALSE)

Arguments

series

An OTS.

states

A numerical vector containing the corresponding states.

distance

A function defining the underlying distance between states. The Hamming, block and Euclidean distances are already implemented by means of the arguments "Hamming", "Block" (default) and "Euclidean". Otherwise, a function taking as input two states must be provided.

normalize

Logical. If normalize = FALSE (default), the value of the estimated dispersion is returned. Otherwise, the function returns the normalized estimated dispersion.

Details

Given an OTS of length TT with range S={s0,s1,s2,,sn}\mathcal{S}=\{s_0, s_1, s_2, \ldots, s_n\} (s0<s1<s2<<sns_0 < s_1 < s_2 < \ldots < s_n), Xt={X1,,XT}\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}, the function computes the DIVC estimated dispersion given by disp^d=TT1i,j=0nd(si,sj)p^ip^j\widehat{disp}_{d}=\frac{T}{T-1}\sum_{i,j=0}^nd\big(s_i, s_j\big)\widehat{p}_i\widehat{p}_j, where d(,)d(\cdot, \cdot) is a distance between ordinal states and p^k\widehat{p}_k is the standard estimate of the marginal probability for state sks_k. If normalize = TRUE, and distance = "Block" or distance = "Euclidean", then the normalized versions are computed, that is, the corresponding estimates are divided by the factors 2/m2/m or 2/m22/m^2, respectively.

Value

The estimated dispersion according to the approach based on the diversity coefficient.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Weiß CH (2019). “Distance-based analysis of ordinal data and ordinal time series.” Journal of the American Statistical Association.

Examples

estimated_dispersion <- ordinal_dispersion_2(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the DIVC dispersion estimate
# for one series in dataset AustrianWages using the block distance

[Package otsfeatures version 1.0.0 Index]