dmixmvbeta {mable}

Multivariate Mixture Beta Distribution

Description

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.

Usage

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.