Marginal density, marginal distribution function, marginal quantile function and random generation for weight functions.
mdone.sided(x, alpha = NULL, alpha1 = NULL, alpha2 = NULL, log = FALSE)
mdtwo.sided(x, alpha, log = FALSE)
mdone.sided_fixed(x, omega, log = FALSE)
mdtwo.sided_fixed(x, omega, log = FALSE)
rone.sided(n, alpha = NULL, alpha1 = NULL, alpha2 = NULL)
rtwo.sided(n, alpha)
rone.sided_fixed(n, omega)
rtwo.sided_fixed(n, omega)
mpone.sided(
q,
alpha = NULL,
alpha1 = NULL,
alpha2 = NULL,
lower.tail = TRUE,
log.p = FALSE
)
mptwo.sided(q, alpha, lower.tail = TRUE, log.p = FALSE)
mpone.sided_fixed(q, omega, lower.tail = TRUE, log.p = FALSE)
mptwo.sided_fixed(q, omega, lower.tail = TRUE, log.p = FALSE)
mqone.sided(
p,
alpha = NULL,
alpha1 = NULL,
alpha2 = NULL,
lower.tail = TRUE,
log.p = FALSE
)
mqtwo.sided(p, alpha, lower.tail = TRUE, log.p = FALSE)
mqone.sided_fixed(p, omega, lower.tail = TRUE, log.p = FALSE)
mqtwo.sided_fixed(p, omega, lower.tail = TRUE, log.p = FALSE)numeric vector of quantiles; the parameter arguments (alpha,
omega) may be matrices with one row per quantile.
vector or matrix with concentration parameters for the Dirichlet distribution for a monotonic one.sided or a two.sided weight function.
vector or matrix with concentration parameters for the Dirichlet distribution for the expected direction of non-monotonic one.sided of weight function.
vector or matrix with concentration parameters for the Dirichlet distribution for the unexpected direction of non-monotonic one.sided of weight function.
logical; if TRUE, probabilities
p are given as log(p).
vector or matrix of fixed non-negative relative weights for a one.sided or a two.sided weight function. The first/reference weight must be exactly 1.
number of observations.
logical; if TRUE (default), probabilities
are \(P[X \le x]\), otherwise, \(P[X > x]\).
vector of probabilities.
mdone.sided, mdtwo.sided, mdone.sided_fixed,
and mdtwo.sided_fixed give the marginal density,
mpone.sided, mptwo.sided, mpone.sided_fixed,
and mptwo.sided_fixed give the marginal distribution function,
mqone.sided, mqtwo.sided, mqone.sided_fixed,
and mqtwo.sided_fixed give the marginal quantile function,
and rone.sided, rtwo.sided, rone.sided_fixed,
and rtwo.sided_fixed generate random deviates.
The marginal density, distribution function, and quantile function
are implemented for the monotonic parameterization (alpha) and for
fixed weights (omega); the non-monotonic parameterization
(alpha1, alpha2) supports random generation only. The same
marginals of a prior_weightfunction() prior are available through
mpdf(), mcdf(), mquant(), and rng().
The marginals of the monotonic parameterization are Beta distributions with
the cumulative sums of alpha as shapes. Finite alpha whose
cumulative sums exceed the largest double signal an error of class
BayesTools_weightfunction_beta_shape_unavailable (parent
BayesTools_weightfunction_unavailable) from the density,
distribution, and quantile functions, and from mpdf(), mcdf(), and
mquant() of a cumulative prior_weightfunction(). Degenerate Dirichlet
draws of the random generation signal
BayesTools_dirichlet_rng_unavailable.
# draw samples from a two-sided weight function
rtwo.sided(10, alpha = c(1, 1))
#> [,1] [,2]
#> [1,] 1 0.38158741
#> [2,] 1 0.65898459
#> [3,] 1 0.26455932
#> [4,] 1 0.57377765
#> [5,] 1 0.94413481
#> [6,] 1 0.58500214
#> [7,] 1 0.08396359
#> [8,] 1 0.91470460
#> [9,] 1 0.62069994
#> [10,] 1 0.81284209
# draw samples from a monotone one-sided weight function
rone.sided(10, alpha = c(1, 1, 1))
#> [,1] [,2] [,3]
#> [1,] 1 0.9608803 0.8769134
#> [2,] 1 0.9759831 0.6407324
#> [3,] 1 0.2634984 0.2171226
#> [4,] 1 0.7707671 0.1587757
#> [5,] 1 0.5712306 0.4731679
#> [6,] 1 0.4843504 0.4602232
#> [7,] 1 0.8653360 0.8201653
#> [8,] 1 0.8242785 0.1804111
#> [9,] 1 0.6590175 0.5818302
#> [10,] 1 0.4794643 0.1021826
# draw samples from a non-monotone one-sided weight function
rone.sided(10, alpha1 = c(1, 1), alpha2 = c(1, 1))
#> [,1] [,2] [,3]
#> [1,] 1 0.90100116 0.9731780
#> [2,] 1 0.10270708 0.4825053
#> [3,] 1 0.82844974 0.8380465
#> [4,] 1 0.29140310 0.4802061
#> [5,] 1 0.72345174 0.9878073
#> [6,] 1 0.03404128 0.8208037
#> [7,] 1 0.90546006 0.9595856
#> [8,] 1 0.89529970 0.9757184
#> [9,] 1 0.21524578 0.9436983
#> [10,] 1 0.91385254 0.9820721