LognormalTrunc {EnvStats} | R Documentation |
The Truncated Lognormal Distribution
Description
Density, distribution function, quantile function, and random generation
for the truncated lognormal distribution with parameters meanlog
,
sdlog
, min
, and max
.
Usage
dlnormTrunc(x, meanlog = 0, sdlog = 1, min = 0, max = Inf)
plnormTrunc(q, meanlog = 0, sdlog = 1, min = 0, max = Inf)
qlnormTrunc(p, meanlog = 0, sdlog = 1, min = 0, max = Inf)
rlnormTrunc(n, meanlog = 0, sdlog = 1, min = 0, max = Inf)
Arguments
x |
vector of quantiles. |
q |
vector of quantiles. |
p |
vector of probabilities between 0 and 1. |
n |
sample size. If |
meanlog |
vector of means of the distribution of the non-truncated random variable
on the log scale.
The default is |
sdlog |
vector of (positive) standard deviations of the non-truncated random variable
on the log scale.
The default is |
min |
vector of minimum values for truncation on the left. The default value is
|
max |
vector of maximum values for truncation on the right. The default value is
|
Details
See the help file for the lognormal distribution for information about the density and cdf of a lognormal distribution.
Probability Density and Cumulative Distribution Function
Let denote a random variable with density function
and
cumulative distribution function
, and let
denote the truncated version of
where
is truncated
below at
min=
and above at
max=
. Then the density
function of
, denoted
, is given by:
and the cdf of Y, denoted , is given by:
| 0 | for |
| for |
|
1 | for |
|
Quantiles
The quantile
of
is given by:
| | for |
| for |
|
| for |
|
Random Numbers
Random numbers are generated using the inverse transformation method:
where is a random deviate from a uniform
distribution.
Value
dlnormTrunc
gives the density, plnormTrunc
gives the distribution function,
qlnormTrunc
gives the quantile function, and rlnormTrunc
generates random
deviates.
Note
A truncated lognormal distribution is sometimes used as an input distribution for probabilistic risk assessment.
Author(s)
Steven P. Millard (EnvStats@ProbStatInfo.com)
References
Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.
Johnson, N. L., S. Kotz, and N. Balakrishnan. (1994). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.
Schneider, H. (1986). Truncated and Censored Samples from Normal Populations. Marcel Dekker, New York, Chapter 2.
See Also
Lognormal, Probability Distributions and Random Numbers.
Examples
# Density of a truncated lognormal distribution with parameters
# meanlog=1, sdlog=0.75, min=0, max=10, evaluated at 2 and 4:
dlnormTrunc(c(2, 4), 1, 0.75, 0, 10)
#[1] 0.2551219 0.1214676
#----------
# The cdf of a truncated lognormal distribution with parameters
# meanlog=1, sdlog=0.75, min=0, max=10, evaluated at 2 and 4:
plnormTrunc(c(2, 4), 1, 0.75, 0, 10)
#[1] 0.3558867 0.7266934
#----------
# The median of a truncated lognormal distribution with parameters
# meanlog=1, sdlog=0.75, min=0, max=10:
qlnormTrunc(.5, 1, 0.75, 0, 10)
#[1] 2.614945
#----------
# A random sample of 3 observations from a truncated lognormal distribution
# with parameters meanlog=1, sdlog=0.75, min=0, max=10.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(20)
rlnormTrunc(3, 1, 0.75, 0, 10)
#[1] 5.754805 4.372218 1.706815