dcomper {dsfa} | R Documentation |
Probablitiy density function, distribution, quantile function and random number generation for the composed-error distribution
dcomper(
x,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
distr = "normhnorm",
deriv_order = 0,
tri = NULL,
log.p = FALSE
)
pcomper(
q,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
distr = "normhnorm",
deriv_order = 0,
tri = NULL,
log.p = FALSE
)
qcomper(
p,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
distr = "normhnorm",
log.p = FALSE
)
rcomper(n, mu = 0, sigma_v = 1, sigma_u = 1, s = -1, distr = "normhnorm")
x |
numeric vector of quantiles. |
mu |
numeric vector of |
sigma_v |
numeric vector of |
sigma_u |
numeric vector of |
s |
integer; |
distr |
string; determines the distribution: |
deriv_order |
integer; maximum order of derivative. Available are |
tri |
optional; index matrix for upper triangular, generated by |
log.p |
logical; if TRUE, probabilities p are given as log(p). |
q |
numeric vector of quantiles. |
p |
numeric vector of probabilities. |
n |
positive integer; number of observations. |
This is wrapper function for the normal-halfnormal and normal-exponential distribution. A random variable X
follows a composed error distribution if X = V + s \cdot U
, where V \sim N(\mu, \sigma_V^2)
and U \sim HN(0,\sigma_U^2)
or U \sim Exp(\sigma_U^2)
.
For more details see dnormhnorm()
and dnormexp()
. Here, s=-1
for production and s=1
for cost function.
dcomper()
gives the density, pcomper()
give the distribution function, qcomper()
gives the quantile function, and rcomper()
generates random numbers, with given parameters.
dcomper()
and pcomper()
return a derivs
object.
pcomper()
: distribution function for the composed-error distribution.
qcomper()
: quantile function for the composed-error distribution.
rcomper()
: random number generation for the composed-error distribution.
Aigner D, Lovell CK, Schmidt P (1977). “Formulation and estimation of stochastic frontier production function models.” Journal of econometrics, 6(1), 21–37.
Kumbhakar SC, Wang H, Horncastle AP (2015). A practitioner's guide to stochastic frontier analysis using Stata. Cambridge University Press.
Schmidt R, Kneib T (2020). “Analytic expressions for the Cumulative Distribution Function of the Composed Error Term in Stochastic Frontier Analysis with Truncated Normal and Exponential Inefficiencies.” arXiv preprint arXiv:2006.03459.
Gradshteyn IS, Ryzhik IM (2014). Table of integrals, series, and products. Academic press.
Azzalini A (2013). The skew-normal and related families, volume 3. Cambridge University Press.
Other distribution:
dcomper_mv()
,
dnormexp()
,
dnormhnorm()
pdf <- dcomper(x=5, mu=1, sigma_v=2, sigma_u=3, s=-1, distr="normhnorm")
cdf <- pcomper(q=5, mu=1, sigma_v=2, sigma_u=3, s=-1, distr="normhnorm")
q <- qcomper(p=seq(0.1, 0.9, by=0.1), mu=1, sigma_v=2, sigma_u=3, s=-1, distr="normhnorm")
r <- rcomper(n=10, mu=1, sigma_v=2, sigma_u=3, s=-1, distr="normhnorm")