dpairbeta function

Pairwise Beta (PB) and Nested Asymmetric Logistic (NL) distributions

Likelihood function (spectral density) and random generator in the Pairwise Beta and NL models.

dnestlog(
  x = rbind(c(0.1, 0.3, 0.6), c(0.3, 0.3, 0.4)),
  par = c(0.5, 0.5, 0.2, 0.3),
  log = FALSE,
  vectorial = TRUE
)

dpairbeta(
  x,
  par = c(1, rep(2, choose(4, 2) + 1)),
  log = FALSE,
  vectorial = TRUE
)

rnestlog(
  n = 5,
  par = c(0.2, 0.3, 0.4, 0.5),
  threshold = 1000,
  return.points = FALSE
)

rpairbeta(n = 1, dimData = 3, par = c(1, rep(1, 3)))

Arguments

• x: An angular data set (may be reduced to a single point). A npoints*dimData matrix (or a vector of length(dimData). For the NL model, dimData is always $3$. Each row is a point on the simplex, so that the sum of each rows should equal $1$ (the error tolerance is set to 1e-8

  in this package).

• par: The parameter for the Pairwise Beta or the Nested Logistic density.

  • In the Pairwise Beta model, par is of length choose(p,2)+1. The first element is the global dependence parameter, the subsequent ones are the pairwise dependence parameters, in lexicographic order (e.g.

    $\beta_{12}, \beta_{13}, \beta_{23}$).

  • In the NL model, par is a vector of length four with components between zero and one. The first one is the global dependence parameter, the three subsequent ones are the pairwise dependence parameters, again in lexicographic order.

• log: Logical. Should the density be returned on the log scale ?

• vectorial: Logical. Should a vector or a single value be returned ?

• n: The number of points on the simplex to be generated.

• threshold: The radial threshold $r$ above which the simulated points should be kept to build the angular dataset. Should be set to a high value, for the asymptotic approximation

to hold.

• return.points: logical: should the censored vectorial dataset corresponding to the angular one be returned ?
• dimData: the dimension of the sample space, which is $1 +$ the dimension of the simplex.

Returns

The value returned by the likelihood function is imposed (see e.g. posteriorMCMC. In contrast, the random variable have unconstrained output format.

• dpairbeta returns the likelihood as a single number if vectorial ==FALSE, or as a vector of size nrow(x) containing the likelihood of each angular data point. If log == TRUE, the log-likelihood is returned instead. rpairbeta returns a matrix with n

  rows and dimData columns.

• dnestlog returns the likelihood as a single number if vectorial ==FALSE, or as a vector of size nrow(x) containing the likelihood of each angular data point. If log == TRUE, the log-likelihood is returned instead. rnestlog returns a matrix with n rows and dimData columns if return.points==FALSE (the default). Otherwise, a list is returned, with two elements:

  • Angles: The angular data set

  • Points: The full tri-variate data set above threshold (i.e. Angles

    multiplied by the radial components)

Details

Applies to angular data sets. The density is given with respect to the Lebesgue measure on $R^(p-1)$, where p is the number of columns in x (or the length of x, if the latter is a single point).