LognormalTruncAlt {EnvStats}  R Documentation 
Density, distribution function, quantile function, and random generation
for the truncated lognormal distribution with parameters mean
,
cv
, min
, and max
.
dlnormTruncAlt(x, mean = exp(1/2), cv = sqrt(exp(1)  1), min = 0, max = Inf)
plnormTruncAlt(q, mean = exp(1/2), cv = sqrt(exp(1)  1), min = 0, max = Inf)
qlnormTruncAlt(p, mean = exp(1/2), cv = sqrt(exp(1)  1), min = 0, max = Inf)
rlnormTruncAlt(n, mean = exp(1/2), cv = sqrt(exp(1)  1), min = 0, max = Inf)
x 
vector of quantiles. 
q 
vector of quantiles. 
p 
vector of probabilities between 0 and 1. 
n 
sample size. If 
mean 
vector of means of the distribution of the nontruncated random variable.
The default is 
cv 
vector of (positive) coefficient of variations of the nontruncated random variable.
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

See the help file for LognormalAlt for information about the density and cdf of a lognormal distribution with this alternative parameterization.
Let X
denote a random variable with density function f(x)
and
cumulative distribution function F(x)
, and let
Y
denote the truncated version of X
where Y
is truncated
below at min=
A
and above atmax=
B
. Then the density
function of Y
, denoted g(y)
, is given by:
g(y) = frac{f(y)}{F(B)  F(A)}, A \le y \le B
and the cdf of Y, denoted G(y)
, is given by:
G(y) =  0  for y < A 
\frac{F(y)  F(A)}{F(B)  F(A)}  for A \le y \le B 

1  for y > B 

The p^{th}
quantile y_p
of Y
is given by:
y_p =  A  for p = 0 
F^{1}\{p[F(B)  F(A)] + F(A)\}  for 0 < p < 1 

B  for p = 1 

Random numbers are generated using the inverse transformation method:
y = G^{1}(u)
where u
is a random deviate from a uniform [0, 1]
distribution.
dlnormTruncAlt
gives the density, plnormTruncAlt
gives the distribution function,
qlnormTruncAlt
gives the quantile function, and rlnormTruncAlt
generates random
deviates.
A truncated lognormal distribution is sometimes used as an input distribution for probabilistic risk assessment.
Steven P. Millard (EnvStats@ProbStatInfo.com)
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.
LognormalAlt, Probability Distributions and Random Numbers.
# Density of a truncated lognormal distribution with parameters
# mean=10, cv=1, min=0, max=20, evaluated at 2 and 12:
dlnormTruncAlt(c(2, 12), 10, 1, 0, 20)
#[1] 0.08480874 0.03649884
#
# The cdf of a truncated lognormal distribution with parameters
# mean=10, cv=1, min=0, max=20, evaluated at 2 and 12:
plnormTruncAlt(c(2, 4), 10, 1, 0, 20)
#[1] 0.07230627 0.82467603
#
# The median of a truncated lognormal distribution with parameters
# mean=10, cv=1, min=0, max=20:
qlnormTruncAlt(.5, 10, 1, 0, 20)
#[1] 6.329505
#
# A random sample of 3 observations from a truncated lognormal distribution
# with parameters mean=10, cv=1, min=0, max=20.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(20)
rlnormTruncAlt(3, 10, 1, 0, 20)
#[1] 6.685391 17.445387 18.543553