dsfa (version 2.0.2)

dcomper: Composed-Error distribution

Description

Probablitiy density function, distribution, quantile function and random number generation for the composed-error distribution

Usage

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")

Value

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() returns a derivs object.

Arguments

x

numeric vector of quantiles.

mu

numeric vector of \(\mu\).

sigma_v

numeric vector of \(\sigma_V\). Must be positive.

sigma_u

numeric vector of \(\sigma_U\). Must be positive.

s

integer; \(s=-1\) for production and \(s=1\) for cost function.

distr

string; determines the distribution:
`normhnorm`, Normal-halfnormal distribution
`normexp`, Normal-exponential distribution

deriv_order

integer; maximum order of derivative. Available are 0,2 and 4.

tri

optional; index matrix for upper triangular, generated by trind_generator.

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.

Functions

• 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.

Details

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.

References

• aigner1977formulationdsfa

• kumbhakar2015practitionerdsfa

• schmidt2020analyticdsfa

• gradshteyn2014tabledsfa

• azzalini2013skewdsfa

See Also

Other distribution: dcomper_mv(), dnormexp(), dnormhnorm()

Examples

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")