tlnorm: The truncated log-normal distribution

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

The truncated log-normal distribution

Description

Density, distribution function, quantile function and random generation for the truncated log-normal distribution.

Usage

dtlnorm(x, meanlog = 0, sdlog = 1, endpoint = Inf, log = FALSE)
ptlnorm(x, meanlog = 0, sdlog = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtlnorm(p, meanlog = 0, sdlog = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtlnorm(n, meanlog = 0, sdlog = 1, endpoint = Inf)

Arguments

x	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
meanlog	Mean of the distribution on the log scale, default is 0.
sdlog	Standard deviation of the distribution on the log scale, default is 1.
endpoint	Endpoint of the truncated log-normal distribution. The default value is Inf for which the truncated log-normal distribution corresponds to the ordinary log-normal distribution.
log	Logical indicating if the densities are given as \log(f), default is FALSE.
lower.tail	Logical indicating if the probabilities are of the form P(X\le x) (TRUE) or P(X>x) (FALSE). Default is TRUE.
log.p	Logical indicating if the probabilities are given as \log(p), default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the truncated log-normal distribution is equal to F_T(x) = F(x) / F(T) for x \le T where F is the CDF of the ordinary log-normal distribution and T is the endpoint (truncation point) of the truncated log-normal distribution.

Value

dtlnorm gives the density function evaluated in x, ptlnorm the CDF evaluated in x and qtlnorm the quantile function evaluated in p. The length of the result is equal to the length of x or p.

rtlnorm returns a random sample of length n.

Author(s)

Tom Reynkens.

See Also

Lognormal, Distributions

Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtlnorm(x, endpoint=9), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptlnorm(x, endpoint=9), xlab="x", ylab="CDF", type="l")

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.