dcomper {dsfa} R Documentation

## 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

• 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")