marginal_probabilities: Computes the marginal probabilities of an ordinal time series
Description
marginal_probabilities returns a vector with the marginal
probabilities of an ordinal time series
Usage
marginal_probabilities(series, states)
Value
A vector with the marginal probabilities.
Arguments
series
An OTS (numerical vector with integers).
states
A numerical vector containing the corresponding
states
Author
Ángel López-Oriona, José A. Vilar
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
vector \(\widehat{\boldsymbol p} =(\widehat{p}_0, \ldots, \widehat{p}_n)\),
with \(\widehat{p}_i=\frac{N_i}{T}\), where \(N_i\) is the number
of elements equal to \(s_i\) in the realization \(\overline{X}_t\).
vector_mp <- marginal_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the vector of# marginal probabilities for one series in dataset AustrianWages