lno: The Log-Normal Distribution

In rdmatheus/BCNSM: Multivariate Box-Cox Symmetric Distributions Generated by a Normal Scale Mixture Copula

The Log-Normal Distribution

Description

Density, distribution function, quantile function, and random generation for the log-normal distribution with parameters mu and sigma.

Usage

dlno(x, mu, sigma, log = FALSE, ...)

plno(q, mu, sigma, lower.tail = TRUE, ...)

qlno(p, mu, sigma, lower.tail = TRUE, ...)

rlno(n, mu, sigma)

Arguments

x, q	vector of positive quantiles.
mu	vector of strictly positive scale parameters.
sigma	vector of strictly positive relative dispersion parameters.
log	logical; if TRUE, probabilities p are given as log(p).
...	further arguments.
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of random values to return.

Details

A random variable X has a log-normal distribution with parameter mu and sigma if log(X) follows a normal distribution with location parameter log(mu) and dispersion parameter sigma. It can be showed that mu is the median of X.

Value

dlno returns the density, plno gives the distribution function, qlno gives the quantile function, and rlno generates random observations.

Invalid arguments will result in return value NaN.

The length of the result is determined by n for rlno, and is the maximum of the lengths of the numerical arguments for the other functions.

Author(s)

Rodrigo M. R. de Medeiros <[e-mail]>

References

Vanegas, L. H., and Paula, G. A. (2016). Log-symmetric distributions: statistical properties and parameter estimation. Brazilian Journal of Probability and Statistics, 30, 196-220.

Examples

mu <- 8
sigma <- 1

# Sample generation
x <- rlno(10000, mu, sigma)

# Density
hist(x, prob = TRUE, main = "The Log-Normal Distribution", col = "white")
curve(dlno(x, mu, sigma), add = TRUE, col = 2, lwd = 2)
legend("topright", "Probability density function", col = 2, lwd = 2, lty = 1)

# Distribution function
plot(ecdf(x), main = "The Log-Normal Distribution", ylab = "Distribution function")
curve(plno(x, mu, sigma), add = TRUE, col = 2, lwd = 2)
legend("bottomright", c("Emp. distribution function", "Theo. distribution function"),
  col = c(1, 2), lwd = 2, lty = c(1, 1)
)

# Quantile function
plot(seq(0.01, 0.99, 0.001), quantile(x, seq(0.01, 0.99, 0.001)),
  type = "l",
  xlab = "p", ylab = "Quantile function", main = "The Log-Normal Distribution"
)
curve(qlno(x, mu, sigma), add = TRUE, col = 2, lwd = 2, from = 0, to = 1)
legend("topleft", c("Emp. quantile function", "Theo. quantile function"),
  col = c(1, 2), lwd = 2, lty = c(1, 1)
)

rdmatheus/BCNSM documentation built on Feb. 8, 2024, 1:28 a.m.