dnormexp {dsfa}R Documentation

Normal-Exponential distribution

Description

Probablitiy density function, distribution, quantile function and random number generation for the normal-exponential distribution

Usage

dnormexp(
  x,
  mu = 0,
  sigma_v = 1,
  sigma_u = 1,
  s = -1,
  deriv_order = 0,
  tri = NULL,
  log.p = FALSE
)

pnormexp(
  q,
  mu = 0,
  sigma_v = 1,
  sigma_u = 1,
  s = -1,
  deriv_order = 0,
  tri = NULL,
  log.p = FALSE
)

qnormexp(p, mu = 0, sigma_v = 1, sigma_u = 1, s = -1, log.p = FALSE)

rnormexp(n, mu = 0, sigma_v = 1, sigma_u = 1, s = -1)

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.

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

A random variable X follows a normal-exponential distribution if X = V + s \cdot U , where V \sim N(\mu, \sigma_V^2) and U \sim Exp(\sigma_u). The density is given by

f_X(x)=\frac{\sigma_U}{2} \exp \{\sigma_U (s \mu) + \frac{1}{2} \sigma_U^2 \sigma_V^2-\sigma_U (s x) \} 2 \Phi(\frac{1}{\sigma_V} (-s \mu)-\sigma_U \sigma_V+\frac{1}{\sigma_V}(s x)) \qquad,

where s=-1 for production and s=1 for cost function. In the latter case the distribution is equivalent to the Exponentially modified Gaussian distribution.

Value

dnormexp() gives the density, pnormexp() give the distribution function, qnormexp() gives the quantile function, and rnormexp() generates random numbers, with given parameters. dnormexp() and pnormexp() return a derivs object. For more details see trind() and trind_generator().

Functions

References

See Also

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

Examples

pdf <- dnormexp(x=5, mu=1, sigma_v=2, sigma_u=3, s=-1)
cdf <- pnormexp(q=5, mu=1, sigma_v=2, sigma_u=3, s=-1)
q <- qnormexp(p=seq(0.1, 0.9, by=0.1), mu=1, sigma_v=2, sigma_u=3, s=-1)
r <- rnormexp(n=10, mu=1, sigma_v=2, sigma_u=3, s=-1)


[Package dsfa version 2.0.1 Index]