Description Usage Arguments Details Value Note Author(s) References See Also Examples
Estimate the mean and standard deviation parameters of the logarithm of a lognormal distribution, and optionally construct a confidence interval for the mean.
1 2 
x 
numeric vector of observations. 
method 
character string specifying the method of estimation. Possible values are

ci 
logical scalar indicating whether to compute a confidence interval for the
mean. The default value is 
ci.type 
character string indicating what kind of confidence interval to compute. The
possible values are 
ci.method 
character string indicating what method to use to construct the confidence interval
for the mean or variance. The only possible value is 
conf.level 
a scalar between 0 and 1 indicating the confidence level of the confidence interval.
The default value is 
If x
contains any missing (NA
), undefined (NaN
) or
infinite (Inf
, Inf
) values, they will be removed prior to
performing the estimation.
Let X denote a random variable with a
lognormal distribution with
parameters meanlog=
μ and sdlog=
σ. Then
Y = log(X) has a normal (Gaussian) distribution with
parameters mean=
μ and sd=
σ. Thus, the function
elnorm
simply calls the function enorm
using the
logtransformed values of x
.
a list of class "estimate"
containing the estimated parameters and other information.
See
estimate.object
for details.
The normal and lognormal distribution are probably the two most frequently used distributions to model environmental data. In order to make any kind of probability statement about a normallydistributed population (of chemical concentrations for example), you have to first estimate the mean and standard deviation (the population parameters) of the distribution. Once you estimate these parameters, it is often useful to characterize the uncertainty in the estimate of the mean or variance. This is done with confidence intervals.
Steven P. Millard ([email protected])
Aitchison, J., and J.A.C. Brown (1957). The Lognormal Distribution (with special references to its uses in economics). Cambridge University Press, London, Chapter 5.
Crow, E.L., and K. Shimizu. (1988). Lognormal Distributions: Theory and Applications. Marcel Dekker, New York, Chapter 2.
Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.
Gilbert, R.O. (1987). Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold, New York, NY.
Johnson, N. L., S. Kotz, and N. Balakrishnan. (1994). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.
Limpert, E., W.A. Stahel, and M. Abbt. (2001). LogNormal Distributions Across the Sciences: Keys and Clues. BioScience 51, 341–352.
Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with SPLUS. CRC Press, Boca Raton, FL.
Ott, W.R. (1995). Environmental Statistics and Data Analysis. Lewis Publishers, Boca Raton, FL.
USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R09007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C.
Lognormal, LognormalAlt, Normal.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  # Using the Reference area TcCB data in the data frame EPA.94b.tccb.df,
# estimate the mean and standard deviation of the logtransformed distribution,
# and construct a 95% confidence interval for the mean.
with(EPA.94b.tccb.df, elnorm(TcCB[Area == "Reference"], ci = TRUE))
#Results of Distribution Parameter Estimation
#
#
#Assumed Distribution: Lognormal
#
#Estimated Parameter(s): meanlog = 0.6195712
# sdlog = 0.4679530
#
#Estimation Method: mvue
#
#Data: TcCB[Area == "Reference"]
#
#Sample Size: 47
#
#Confidence Interval for: mean
#
#Confidence Interval Method: Exact
#
#Confidence Interval Type: twosided
#
#Confidence Level: 95%
#
#Confidence Interval: LCL = 0.7569673
# UCL = 0.4821751

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