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

• pcomperr_mv(): distribution function for the composed error multivariate distribution.

• rcomperr_mv(): random number generation for the composed error multivariate distribution.

References

• Aigner D, Lovell CK, Schmidt P (1977). “Formulation and estimation of stochastic frontier production function models.” Journal of econometrics, 6(1), 21–37.

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)

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