qlnorm3: qlnorm3: The Lognormal Distribution (3 Parameter)

In r6qualitytools: R6-Based Statistical Methods for Quality Science

qlnorm3: The Lognormal Distribution (3 Parameter)

Description

Density function, distribution function, and quantile function for the Lognormal distribution.

Usage

qlnorm3(p, meanlog, sdlog, threshold, ...)

Arguments

p	A numeric vector of probabilities.
meanlog, sdlog	The mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.
threshold	The threshold parameter, default is 0.
...	Additional arguments that can be passed to uniroot.

Details

The Lognormal distribution with meanlog parameter zeta, sdlog parameter sigma, and threshold parameter theta has a density given by:

f(x) = \frac{1}{\sqrt{2\pi}\sigma(x-\theta)}\exp\left(-\frac{(\log(x-\theta)-\zeta)^2}{2\sigma^2}\right)

The cumulative distribution function is given by:

F(x) = \Phi\left(\frac{\log(x-\theta)-\zeta}{\sigma}\right)

where \Phi is the cumulative distribution function of the standard normal distribution.

Value

dlnorm3 gives the density, plnorm3 gives the distribution function, and qlnorm3 gives the quantile function.

Examples

dlnorm3(x = 2, meanlog = 0, sdlog = 1/8, threshold = 1)
temp <- plnorm3(q = 2, meanlog = 0, sdlog = 1/8, threshold = 1)
temp
qlnorm3(p = temp, meanlog = 0, sdlog = 1/8, threshold = 1)

r6qualitytools documentation built on Oct. 4, 2024, 1:09 a.m.