Lognormalb: The Log Normal Distribution parameterized through its mean and standard deviation.

Description

Density, distribution function, quantile function and random generation for a log normal distribution whose arithmetic mean equals to mean and standard deviation equals to sd.

Usage

dlnormb(x, mean = exp(0.5), sd = sqrt(exp(2) - exp(1)), log = FALSE)
plnormb(
  q,
  mean = exp(0.5),
  sd = sqrt(exp(2) - exp(1)),
  lower.tail = TRUE,
  log.p = FALSE
)
qlnormb(
  p,
  mean = exp(0.5),
  sd = sqrt(exp(2) - exp(1)),
  lower.tail = TRUE,
  log.p = FALSE
)
rlnormb(n, mean = exp(0.5), sd = sqrt(exp(2) - exp(1)))

Value

dlnormb gives the density, plnormb gives the distribution function, qlnormb gives the quantile function, and rlnormb generates random deviates. The length of the result is determined by n for rlnorm, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

The default mean and sd are chosen to provide a distribution close to a lognormal with meanlog = 0 and sdlog = 1.

Arguments

x, q: vector of quantiles.
mean: the mean of the distribution.
sd: the standard deviation of the distribution.
log, log.p: logical. if `TRUE` probabilities `p` are given as `log(p)`.
lower.tail: logical. if `TRUE`, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
p: vector of probabilities.
n: number of observations. If `length(n) > 1`, the length is taken to be the number required.

Details

This function calls the corresponding density, distribution function, quantile function and random generation from the log normal (see Lognormal) after evaluation of \(meanlog = log(mean^2 / sqrt(sd^2+mean^2))\) and \(sqrt{(log(1+sd^2/mean^2))}\)

Examples

Run this code

x <- rlnormb(1E5,3,6)
mean(x) 
sd(x)
dlnormb(1) == dnorm(0)
dlnormb(1) == dlnorm(1)