Description Usage Arguments Details Value Author(s) See Also Examples
These functions provide the density, distribution function, quantile function, and random generation for the univariate log-normal distribution with mean mu and precision tau.
1 2 3 4 |
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 mu. |
tau |
This is the precision parameter tau, which must be positive. Tau and var cannot be used together |
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(tau/(2*pi)) * (1/theta) * exp(-(tau/2)*(log(theta-mu))^2)
Inventor: Carl Friedrich Gauss or Abraham De Moivre
Notation 1: theta ~ Log-N(mu, tau^(-1))
Notation 2: p(theta) = Log-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 -> 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
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 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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