Density, distribution function, and
pseudorandom number generation for the multivariate Bernstein polynomial model,
mixture of multivariate beta distributions, with given mixture proportions
\(p = (p_0, \ldots, p_{K-1})\), given degrees \(m = (m_1, \ldots, m_d)\),
and support interval.
dmixmvbeta(x, p, m, interval = NULL)pmixmvbeta(x, p, m, interval = NULL)
rmixmvbeta(n, p, m, interval = NULL)
a matrix with d columns or a vector of length d within
support hyperrectangle \([a, b] = [a_1, b_1] \times \cdots \times [a_d, b_d]\)
a vector of K values. All components of p must be
nonnegative and sum to one for the mixture multivariate beta distribution. See 'Details'.
a vector of degrees, \((m_1, \ldots, m_d)\)
a vector of two endpoints or a 2 x d matrix, each column containing
the endpoints of support/truncation interval for each marginal density.
If missing, the i-th column is assigned as c(0,1)).
sample size
dmixmvbeta() returns a linear combination \(f_m\) of \(d\)-variate beta densities
on \([a, b]\), \(\beta_{mj}(x) = \prod_{i=1}^d\beta_{m_i,j_i}[(x_i-a_i)/(b_i-a_i)]/(b_i-a_i)\),
with coefficients \(p(j_1, \ldots, j_d)\), \(0 \le j_i \le m_i, i = 1, \ldots, d\), where
\([a, b] = [a_1, b_1] \times \cdots \times [a_d, b_d]\) is a hyperrectangle, and the
coefficients are arranged in the column-major order of \(j = (j_1, \ldots, j_d)\),
\(p_0, \ldots, p_{K-1}\), where \(K = \prod_{i=1}^d (m_i+1)\).
pmixmvbeta() returns a linear combination \(F_m\) of the distribution
functions of \(d\)-variate beta distribution.
If all \(p_i\)'s are nonnegative and sum to one, then p
are the mixture proportions of the mixture multivariate beta distribution.