dist.Log.Normal.Precision | R Documentation |
These functions provide the density, distribution function, quantile
function, and random generation for the univariate log-normal
distribution with mean \mu
and precision \tau
.
dlnormp(x, mu, tau=NULL, var=NULL, log=FALSE)
plnormp(q, mu, tau, lower.tail=TRUE, log.p=FALSE)
qlnormp(p, mu, tau, lower.tail=TRUE, log.p=FALSE)
rlnormp(n, mu, tau=NULL, var=NULL)
x , q |
These are each a vector of quantiles. |
p |
This is a vector of probabilities. |
n |
This is the number of observations, which must be a positive integer that has length 1. |
mu |
This is the mean parameter |
tau |
This is the precision parameter |
var |
This is the variance parameter, which must be positive. Tau and var cannot be used together |
log , log.p |
Logical. If |
lower.tail |
Logical. If |
Application: Continuous Univariate
Density: p(\theta) = \sqrt{\frac{\tau}{2\pi}}
\frac{1}{\theta} \exp(-\frac{\tau}{2} (\log(\theta -
\mu))^2)
Inventor: Carl Friedrich Gauss or Abraham De Moivre
Notation 1: \theta \sim \mathrm{Log-}\mathcal{N}(\mu,
\tau^{-1})
Notation 2: p(\theta) = \mathrm{Log-}\mathcal{N}(\theta | \mu,
\tau^{-1})
Parameter 1: mean parameter \mu
Parameter 2: precision parameter \tau > 0
Mean: E(\theta) = \exp(\mu + \tau^{-1} / 2)
Variance: var(\theta) = (\exp(\tau^{-1}) - 1)\exp(2\mu +
\tau^{-1})
Mode: mode(\theta) = \exp(\mu - \tau^{-1})
The log-normal distribution, also called the Galton distribution, is
applied to a variable whose logarithm is normally-distributed. The
distribution is usually parameterized with mean and variance, or in
Bayesian inference, with mean and precision, where precision is the
inverse of the variance. In contrast, Base R
parameterizes the
log-normal distribution with the mean and standard deviation. These
functions provide the precision parameterization for convenience and
familiarity.
A flat distribution is obtained in the limit as
\tau \rightarrow 0
.
These functions are similar to those in base R
.
dlnormp
gives the density,
plnormp
gives the distribution function,
qlnormp
gives the quantile function, and
rlnormp
generates random deviates.
Statisticat, LLC. software@bayesian-inference.com
dnorm
,
dnormp
,
dnormv
, and
prec2var
.
library(LaplacesDemon)
x <- dlnormp(1,0,1)
x <- plnormp(1,0,1)
x <- qlnormp(0.5,0,1)
x <- rlnormp(100,0,1)
#Plot Probability Functions
x <- seq(from=0.1, to=3, by=0.01)
plot(x, dlnormp(x,0,0.1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dlnormp(x,0,1), type="l", col="green")
lines(x, dlnormp(x,0,5), type="l", col="blue")
legend(2, 0.9, expression(paste(mu==0, ", ", tau==0.1),
paste(mu==0, ", ", tau==1), paste(mu==0, ", ", tau==5)),
lty=c(1,1,1), col=c("red","green","blue"))
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