Skew-Lognormal Distribution — dskewlnorm • extras

The skew-lognormal distribution of a random variable whose natural logarithm follows a Skew-Normal distribution with location locationlog, scale scalelog and shapelog. It reduces to the Log-Normal distribution when shapelog = 0.

Usage

dskewlnorm(
  x,
  locationlog = 0,
  scalelog = 1,
  shapelog = 0,
  log = FALSE,
  ...,
  meanlog,
  sdlog,
  shape
)

pskewlnorm(
  q,
  locationlog = 0,
  scalelog = 1,
  shapelog = 0,
  ...,
  meanlog,
  sdlog,
  shape
)

qskewlnorm(
  p,
  locationlog = 0,
  scalelog = 1,
  shapelog = 0,
  ...,
  meanlog,
  sdlog,
  shape
)

rskewlnorm(
  n = 1,
  locationlog = 0,
  scalelog = 1,
  shapelog = 0,
  ...,
  meanlog,
  sdlog,
  shape
)

Arguments

x: A numeric vector of values.
locationlog: A numeric vector of location parameters of log(x).
scalelog: A non-negative numeric vector of scale parameters of log(x).
shapelog: A numeric vector of shape parameters of log(x). Negative values result in leftward skew, while positive values result in rightward skew.
log: A flag specifying whether to return the log-transformed value.
...: Unused.
meanlog: A numeric vector of location parameters of log(x). Described as "a numeric vector of the means on the log scale" prior to v. 0.10.1. Will be removed in a future version.
sdlog: A non-negative numeric vector of scale parameters of log(x). Described as "a non-negative numeric vector of the standard deviations on the log scale" prior to v. 0.10.1. Will be removed in a future version.
shape: A numeric vector of shape parameters of log(x). Will be removed in a future version.
q: A vector of quantiles.
p: A numeric vector of probabilities.
n: A non-negative whole number of the number of random samples to generate.

Value

dskewlnorm gives the density, pskewlnorm gives the distribution function, qskewlnorm gives the quantile function, and rskewlnorm generates random deviates. pskewlnorm and qskewlnorm use the lower tail probability.

Examples

dskewlnorm(x = 1:5, locationlog = 0, scalelog = 1, shapelog = 0.1)
#> [1] 0.39894228 0.16554302 0.07909057 0.04236014 0.02464460
dskewlnorm(x = 1:5, locationlog = 0, scalelog = 1, shapelog = -1)
#> [1] 0.398942280 0.076588593 0.019777519 0.006320389 0.002349402
qskewlnorm(p = c(0.1, 0.4), locationlog = 0, scalelog = 1, shapelog = 0.1)
#> [1] 0.3017701 0.8409793
qskewlnorm(p = c(0.1, 0.4), locationlog = 0, scalelog = 1, shapelog = -1)
#> [1] 0.1954953 0.4704475
pskewlnorm(q = 1:5, locationlog = 0, scalelog = 1, shapelog = 0.1)
#> [1] 0.4682745 0.7309608 0.8467152 0.9050737 0.9375887
pskewlnorm(q = 1:5, locationlog = 0, scalelog = 1, shapelog = -1)
#> [1] 0.7500000 0.9404110 0.9815125 0.9931394 0.9971098
rskewlnorm(n = 3, locationlog = 0, scalelog = 1, shapelog = 0.1)
#> [1] 1.308422 1.327854 1.441730
rskewlnorm(n = 3, locationlog = 0, scalelog = 1, shapelog = -1)
#> [1] 1.1844416 0.3525472 2.8623614