dmixmvbeta function

Multivariate Mixture Beta Distribution

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)

Arguments

• x: a matrix with d columns or a vector of length d within support hyperrectangle $[a, b] = [a_1, b_1] \times \cdots \times [a_d, b_d]$
• p: a vector of K values. All components of p must be nonnegative and sum to one for the mixture multivariate beta distribution. See 'Details'.
• m: a vector of degrees, $(m_1, \ldots, m_d)$
• interval: 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)).
• n: sample size

Details

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.