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r6qualitytools (version 1.0.1)

plnorm3: plnorm3: The Lognormal Distribution (3 Parameter)

Description

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

Usage

plnorm3(q, meanlog, sdlog, threshold)

Value

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

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.

Examples

Run this code
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)

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