dcomperr_mv {dsfa}R Documentation

Composed error multivariate distribution

Description

Probablitiy density function, distribution and random number generation for the composed error multivariate distribution.

Usage

dcomperr_mv(
  x1 = 0,
  mu1 = 0,
  sigma_v1 = 1,
  par_u1 = 1,
  s1 = -1,
  x2 = 0,
  mu2 = 0,
  sigma_v2 = 1,
  par_u2 = 1,
  s2 = -1,
  delta = 0,
  family_mv = c("normhnorm", "normhnorm", "normal"),
  deriv = 0,
  tri = NULL,
  log.p = FALSE,
  check = TRUE
)

pcomperr_mv(
  q1 = 0,
  mu1 = 0,
  sigma_v1 = 1,
  par_u1 = 1,
  s1 = -1,
  q2 = 0,
  mu2 = 0,
  sigma_v2 = 1,
  par_u2 = 1,
  s2 = -1,
  delta = 0,
  family_mv = c("normhnorm", "normhnorm", "normal"),
  log.p = FALSE,
  check = TRUE
)

rcomperr_mv(
  n,
  mu1 = 0,
  sigma_v1 = 1,
  par_u1 = 1,
  s1 = -1,
  mu2 = 0,
  sigma_v2 = 1,
  par_u2 = 1,
  s2 = -1,
  delta = 0,
  family_mv = c("normhnorm", "normhnorm", "normal"),
  check = TRUE
)

Arguments

x1

vector of quantiles for margin 1.

mu1

vector of \mu for margin 1.

sigma_v1

vector of \sigma_V for margin 1. Must be positive.

par_u1

vector of \sigma_U for margin 1. Must be positive.

s1

s=-1 for production and s=1 for cost function for margin 1.

x2

vector of quantiles for margin 2.

mu2

vector of \mu for margin 2.

sigma_v2

vector of \sigma_V for margin 2. Must be positive.

par_u2

vector of \sigma_U for margin 2. Must be positive.

s2

s=-1 for production and s=1 for cost function for margin 2.

delta

matrix of copula parameter. Must have at least one column.

family_mv

string vector, specifying the the margin one and two, as well as the copula. For the margins the distributions normhnorm or normexp are available. For the family_cop:
independent = Independence copula
normal = Gaussian copula
clayton = Clayton copula
gumbel = Gumbel copula
frank = Frank copula
joe = Joe copula

deriv

derivative of order deriv of the log density. Available are 0 and 2.

tri

optional, index arrays for upper triangular matrices, generated by trind.generator() and supplied to chainrule().

log.p

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

check

logical; if TRUE, check inputs.

q1

vector of quantiles for margin 1.

q2

vector of quantiles for margin 2.

n

number of observations.

Details

A bivariate random vector (Y_1,Y_2) follows a composed error multivariate distribution f_{Y_1,Y_2}(y_1,y_2), which can be rewritten using Sklars' theorem via a copula

f_{Y_1,Y_2}(y_1,y_2)=c(F_{Y_1}(y_1),F_{Y_2}(y_2),\delta) \cdot f_{Y_1}(y_1) f_{Y_2}(y_2) \qquad,

where c(\cdot) is a copula function and F_{Y_m}(y_m),f_{Y_m}(y_m) are the marginal cdf and pdf respectively. delta is the copula parameter.

Value

dcomperr_mv gives the density, pcomperr_mv the distribution and rcomperr_mv generates random numbers, with given parameters. If the derivatives are calculated these are provided as the attributes gradient, hessian, l3 and l4 of the output of the density.

Functions

References

Examples

set.seed(1337)
x2<-10;x1<-5
mu2<-7;mu1<-2
sigma_v2<-6;sigma_v1<-3
par_u2<-3;par_u1<-2
s2<-s1<--1
delta<-matrix(0.5,ncol=1, nrow=100)
family_mv=c("normhnorm","normhnorm","normal")

pdf<-dcomperr_mv(x1, mu1, sigma_v1, par_u1, s1,
                 x2, mu2, sigma_v2, par_u2, s2,
                 delta[1, , drop=FALSE], family_mv, deriv = 2, tri=NULL, log.p=FALSE)

cdf<-pcomperr_mv(q1=x1, mu1, sigma_v1, par_u1, s1,
                 q2=x2, mu2, sigma_v2, par_u2, s2,
                 delta[1, , drop=FALSE], family_mv, log.p=FALSE)
r<-rcomperr_mv(n=100, mu1, sigma_v1, par_u1, s1,
               mu2, sigma_v2, par_u2, s2,
               delta, family_mv)


[Package dsfa version 1.0.1 Index]