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)

## Arguments

x, q

vector or matrix of quantiles.

alpha

vector or matrix with concentration parameters for the Dirichlet distribution for a monotonic one.sided or a two.sided weight function.

alpha1

vector or matrix with concentration parameters for the Dirichlet distribution for the expected direction of non-monotonic one.sided of weight function.

alpha2

vector or matrix with concentration parameters for the Dirichlet distribution for the unexpected direction of non-monotonic one.sided of weight function.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

omega

vector or matrix of fixed probabilities for a one.sided or a two.sided weight function.

n

number of observations.

lower.tail

logical; if TRUE (default), probabilities are $$P[X \le x]$$, otherwise, $$P[X \ge x]$$.

p

vector of probabilities.

## Value

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.

## Examples

# draw samples from a two-sided weight function
rtwo.sided(10, alpha = c(1, 1))
#>             [,1] [,2]
#>  [1,] 0.12611583    1
#>  [2,] 0.51534922    1
#>  [3,] 0.03324472    1
#>  [4,] 0.97880318    1
#>  [5,] 0.66200138    1
#>  [6,] 0.23208479    1
#>  [7,] 0.60225018    1
#>  [8,] 0.17453822    1
#>  [9,] 0.06221212    1
#> [10,] 0.37187054    1

# draw samples from a monotone one-sided weight function
rone.sided(10, alpha = c(1, 1, 1))
#>             [,1]      [,2] [,3]
#>  [1,] 0.02844068 0.3728764    1
#>  [2,] 0.10806776 0.2480280    1
#>  [3,] 0.15144097 0.5899361    1
#>  [4,] 0.10568851 0.9009349    1
#>  [5,] 0.33952178 0.5137405    1
#>  [6,] 0.23279764 0.2461865    1
#>  [7,] 0.15653629 0.5081128    1
#>  [8,] 0.05559802 0.8646450    1
#>  [9,] 0.40491313 0.7842544    1
#> [10,] 0.55901682 0.6358587    1

# 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,] 0.9419421 0.92517218    1
#>  [2,] 0.9961456 0.90340682    1
#>  [3,] 0.4788879 0.11089356    1
#>  [4,] 0.3258951 0.22523054    1
#>  [5,] 0.7985171 0.42015953    1
#>  [6,] 0.9908227 0.23165217    1
#>  [7,] 0.9782998 0.55791991    1
#>  [8,] 0.9070065 0.55229814    1
#>  [9,] 0.7060430 0.20216529    1
#> [10,] 0.9672913 0.01495326    1