dnormhnorm {dsfa} | R Documentation |
Probablitiy density function, distribution, quantile function and random number generation for the normal-halfnormal distribution.
dnormhnorm(
x,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
deriv = 0,
tri = NULL,
log.p = FALSE,
check = TRUE
)
pnormhnorm(
q,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
deriv = 0,
tri = NULL,
lower.tail = TRUE,
log.p = FALSE,
check = TRUE
)
qnormhnorm(
p,
mu = 0,
sigma_v = 1,
sigma_u = 1,
s = -1,
lower.tail = TRUE,
log.p = FALSE,
check = TRUE
)
rnormhnorm(n, mu = 0, sigma_v = 1, sigma_u = 1, s = -1, check = TRUE)
x |
vector of quantiles. |
mu |
vector of |
sigma_v |
vector of |
sigma_u |
vector of |
s |
|
deriv |
derivative of order |
tri |
optional, index arrays for upper triangular matrices, generated by |
log.p |
logical; if TRUE, probabilities p are given as log(p). |
check |
logical; if TRUE, check inputs. |
q |
vector of quantiles. |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. |
A random variable \mathcal{E}
follows a normal-halfnormal distribution if \mathcal{E} = V + s \cdot U
, where V \sim N(\mu, \sigma_V^2)
and U \sim HN(\sigma_U^2)
.
The density is given by
f_\mathcal{E}(\epsilon)=\frac{1}{\sqrt{\sigma_V^2+\sigma_U^2}} \phi(\frac{\epsilon-\mu}{\sqrt{\sigma_V^2+\sigma_U^2}}) \Phi(s \frac{\sigma_U}{\sigma_V} \frac{x-\mu}{\sqrt{\sigma_V^2+\sigma_U^2}}) \qquad,
where s=-1
for production and s=1
for cost function.
dnormhnorm
gives the density, pnormhnorm
give the distribution function, qnormhnorm
gives the quantile function, and rnormhnorm
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.
pnormhnorm()
: distribution function for the normal-halfnormal distribution.
qnormhnorm()
: quantile function for the normal-halfnormal distribution.
rnormhnorm()
: random number generation for the normal-halfnormal 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.
pdf <- dnormhnorm(x=seq(-3, 3, by=0.1), mu=1, sigma_v=2, sigma_u=3, s=-1)
cdf <- pnormhnorm(q=seq(-3, 3, by=0.1), mu=1, sigma_v=2, sigma_u=3, s=-1)
q <- qnormhnorm(p=seq(0.1, 0.9, by=0.1), mu=1, sigma_v=2, sigma_u=3, s=-1)
r <- rnormhnorm(n=100, mu=1, sigma_v=2, sigma_u=3, s=-1)