dcomperr_mv {dsfa}  R Documentation 
Probablitiy density function, distribution and random number generation for the composed error multivariate distribution.
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
)
x1 
vector of quantiles for margin 
mu1 
vector of 
sigma_v1 
vector of 
par_u1 
vector of 
s1 

x2 
vector of quantiles for margin 
mu2 
vector of 
sigma_v2 
vector of 
par_u2 
vector of 
s2 

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 
deriv 
derivative of order 
tri 
optional, index arrays for upper triangular matrices, generated by 
log.p 
logical; if 
check 
logical; if TRUE, check inputs. 
q1 
vector of quantiles for margin 1. 
q2 
vector of quantiles for margin 2. 
n 
number of observations. 
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.
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.
pcomperr_mv()
: distribution function for the composed error multivariate distribution.
rcomperr_mv()
: random number generation for the composed error multivariate distribution.
Aigner D, Lovell CK, Schmidt P (1977). “Formulation and estimation of stochastic frontier production function models.” Journal of econometrics, 6(1), 21–37.
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)