Statistical Distributions

dmvnorm(
  x,
  mu = NULL,
  Q,
  detQ = determinant(Q, logarithm = TRUE)$modulus,
  log = TRUE
)

dmvlnorm(
  x,
  mu = NULL,
  Q,
  detQ = determinant(Q, logarithm = TRUE)$modulus,
  log = TRUE
)

dmvnorm_diff(x, y, mu, Q, b, log = TRUE, byrow = FALSE)

dmvlnorm_diff(x, y, mu, Q, log = TRUE, byrow = FALSE)

dnorm_diff(x, y, mu, tau, log = TRUE, byrow = FALSE)

dlnorm_diff(x, y, mu, tau, log = TRUE, byrow = FALSE)

dmatnorm(
  x,
  mu = NULL,
  V,
  U = NULL,
  detV = determinant(V, logarithm = TRUE)$modulus,
  detU = determinant(U, logarithm = TRUE)$modulus,
  log = TRUE
)

dmatnorm_diff(x, y, mu, V, U = NULL, log = TRUE)

dlogitnorm(x, mu, sd, log = FALSE)

rdirich(n, alpha)

rdlnorm(n, meanlog = 0, sdlog = 1)

ddlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)

pdlnorm(x, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)

rtruncexp(n, rate = 1, a = 0, b = Inf)

dtruncexp(x, rate = 1, a = 0, b = Inf, log = FALSE)

ptruncexp(q, rate = 1, a = 0, b = Inf, lower.tail = TRUE, log.p = FALSE)

qtruncexp(p, rate = 1, a = 0, b = Inf)

Arguments

x, y: vector of quantiles
mu: the mean. The default (NULL)- is the same as an appropriately-dimensioned vector/matrix of all zeros, but a little faster.
detQ, detU, detV: Pre-computed log-determinants
log: Should the log-density be returned?
b: Bounds for the truncated exponential distribution or the multivariate normal canonical representation parameter.
byrow: Should the densities be summed (FALSE, the default) or returned separately by row (TRUE).
tau, Q: the precision (matrix)
V, U: the precision matrices for the matrix-normal distribution
sd: the standard deviation
n: Number of deviates to produce.
alpha: the Dirichlet parameter vector or matrix.
meanlog, sdlog: the parameters of the underlying log-normal distribution.
lower.tail: Should lower tail probabilities be returned (default) or upper?
log.p: Should the log be returned?
rate: the Exponential rate parameter. If zero, a normal distribution is used instead. If negative, the problem is flipped and calculated using -rate.
a: Bounds for the truncated exponential distribution.
q: A quantile
p: A probability

Details

dmvnorm_diff(x, y, mu, Q) is equivalent to (but usually twice as fast as) dmvnorm(x, mu, Q) - dmvnorm(y, mu, Q). Likewise dmatnorm_diff.