dcomper: Composed-Error distribution

In dsfa: Distributional Stochastic Frontier Analysis

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")

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.

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.

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.

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.

References

• \insertRef

  aigner1977formulationdsfa

• \insertRef

  kumbhakar2015practitionerdsfa

• \insertRef

  schmidt2020analyticdsfa

• \insertRef

  gradshteyn2014tabledsfa

• \insertRef

  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")

dsfa documentation built on July 26, 2023, 5:51 p.m.