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 |
Details
Given an OTS of length T
with range \mathcal{S}=\{s_0, s_1, s_2, \ldots, s_n\}
(s_0 < s_1 < s_2 < \ldots < s_n
),
\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}
, the function computes the DIVC
estimated dispersion given by \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(\cdot, \cdot)
is a distance between ordinal states and \widehat{p}_k
is the
standard estimate of the marginal probability for state s_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/m
or 2/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