plnorm3: plnorm3: The Lognormal Distribution (3 Parameter)

In r6qualitytools: R6-Based Statistical Methods for Quality Science

plnorm3: The Lognormal Distribution (3 Parameter)

Description

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

Usage

plnorm3(q, meanlog, sdlog, threshold)

Arguments

q	A numeric vector of quantiles.
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.

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.