c_marginal_probabilities: Computes the cumulative marginal probabilities of an ordinal time series
Description
c_marginal_probabilities returns a vector with the cumulative marginal
probabilities of an ordinal time series
Usage
c_marginal_probabilities(series, states)
Value
A vector with the cumulative 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 \(\widehat{\boldsymbol f} =(\widehat{f}_0, \ldots, \widehat{f}_n)\),
with \(\widehat{f}_i=\frac{N_i}{T}\), where \(N_i\) is the number
of elements less than or equal to \(s_i\) in the realization \(\overline{X}_t\).
vector_cmp <- c_marginal_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the vector of# cumulative marginal probabilities for one series in dataset AustrianWages