Description Usage Arguments Details Value Author(s) References Examples
Lognormal models are also widely applied in various branches of natural, social and applied sciences. Given a pair of known constants in the parametric function for the statistics in the lognormal distribution, sample size, degree of freedom of the variance estimation of the log-transformed data, standardized variance of the sampling distribution of the log-transformed data, mean of the log-transformed data and standard deviation of the log-transformed data, this function returns an estimation for the lognormal distribution, including a total of thirty-nine different estimation methods, under a newly proposed unified framework in Zhang and Gou (2020).
1 2 3 4 5 6 7 8 |
data |
original data vector |
estimator |
a total of thirty-eight different estimation methods. See more descriptions in Section Details. |
base |
the base with respect to which logarithms are computed. Defaults to e. |
n |
sample size. |
m |
degree of freedom of the variance estimation of the log-transformed data. |
d |
standardized variance of the sampling distribution of the log-transformed data. |
Consider a parametric function in the original scale we are interested in estimating θ(a,b) = exp(aμ + bσ^2/2),where constants a and b are known. Specifically, θ(1,1) is the mean of the lognormal distribution, θ(2,4) is the second moment, θ(2,4)-θ(2,2) is the variance, and (θ(0,2) - 1)^{1/2} is the coeficient of variation.
unbiased
: Unbiased estimator (Finney, 1941)
qml
: Quasi maximum likelihood estimator
ml
: Maximum likelihood estimator
sa
: Simple adjustment estimator
f
: Finney's unbiased estimator (Finney, 1941)
z
: Zellner's estimator (Zellner, 1971)
es
: Evans and Shaban’s estimator (Evans and Shaban, 1974, 1976)
r-s
: Rukhin’s simple estimator (Rukhin, 1986)
r-f
: Rukhin’s estimator using Finney's function (Rukhin, 1986)
r-lo
: Rukhin’s locally optimal estimator (Rukhin, 1986)
r-b
: Rukhin’s Bayes estimator (Rukhin, 1986)
ev
: El-Shaarawi and Viveros' estimator (El-Shaarawi and Viveros, 1997)
zh
: Zhou's estimator (Zhou, 1998)
sz-mm
: Shen and Zhu's MM estimator (Shen and Zhu, 2008)
sz-mb
: Shen and Zhu's MB estimator (Shen and Zhu, 2008)
l-ub
: Longford's UB estimator (Longford, 2009)
l-ms
: Longford's MS estimator (Longford, 2009)
ft
: Fabrizi and Trivisano's Simplified Bayes estimator (Fabrizi and Trivisano, 2012)
ft-s
: Fabrizi and Trivisano's Simplified Bayes estimator (Fabrizi and Trivisano, 2012)
ft-b
: Fabrizi and Trivisano's Bayes estimator (Fabrizi and Trivisano, 2012)
gt-f
: Gou and Tamhane's estimator using Finney's function (Gou and Tamhane, 2017)
gt-es
: Gou and Tamhane's estimator using Evans and Shaban's function (Gou and Tamhane, 2017)
gt-r
: Gou and Tamhane's estimator using Rukhin's function (Gou and Tamhane, 2017)
zg-1
: Zhang and Gou's first estimator (Zhang and Gou, 2020)
zg-2
: Zhang and Gou's second estimator (Zhang and Gou, 2020)
zg-3
: Zhang and Gou's third estimator (Zhang and Gou, 2020)
zg-4
: Zhang and Gou's fourth estimator (Zhang and Gou, 2020)
zg-5
: Zhang and Gou's fifth estimator (Zhang and Gou, 2020)
zg-6
: Zhang and Gou's sixth estimator (Zhang and Gou, 2020)
zg-7
: Zhang and Gou's seventh estimator (Zhang and Gou, 2020)
zg-8
: Zhang and Gou's eighth estimator (Zhang and Gou, 2020)
zg-9
: Zhang and Gou's ninth estimator (Zhang and Gou, 2020)
zg-10
: Zhang and Gou's tenth estimator (Zhang and Gou, 2020)
zg-11
: Zhang and Gou's eleventh estimator (Zhang and Gou, 2020)
zg-12
: Zhang and Gou's twelveth estimator (Zhang and Gou, 2020)
zg-13
: Zhang and Gou's thirteenth estimator (Zhang and Gou, 2020)
zg-14
: Zhang and Gou's fourteenth estimator (Zhang and Gou, 2020)
zg-15
: Zhang and Gou's fifteenth estimator (Zhang and Gou, 2020)
zg-16
: Zhang and Gou's sixteenth estimator (Zhang and Gou, 2020)
zg-17
: Zhang and Gou's seventeenth estimator (Zhang and Gou, 2020)
zg-18
: Zhang and Gou's eighteenth estimator (Zhang and Gou, 2020)
zg-19
: Zhang and Gou's nineteenth estimator (Zhang and Gou, 2020)
estimated median. .
Jiangtao Gou
Finney, D. J. (1941). On the distribution of a variate whose logarithm is normally distributed. Supplement to the Journal of the Royal Statistical Society, 7: 155-161. <https://doi.org/10.2307/2983663>
Zellner, A. (1971). Bayesian and non-Bayesian analysis of the log-normal distribution and log-normal regression. Journal of the American Statistical Association, 66: 327-330. <https://doi.org/10.1080/01621459.1971.10482263>
Evans, I. G. and Shaban, S. A. (1974). A note on estimation in lognormal models. Journal of the American Statistical Association, 69: 779-781. <https://doi.org/10.2307/2286017>
Rukhin, A. L. (1986). Improved estimation in lognormal models. Journal of the American Statistical Association, 81: 1046-1049. <https://doi.org/10.1080/01621459.1986.10478371>
El-Shaarawi, A. H. and Viveros, R. (1997). Inference about the mean in log-regression with environmental applications. Environmetrics, 8: 569-582. <https://doi.org/10.1002/(SICI)1099-095X(199709/10)8:5<569::AID-ENV274>3.0.CO;2-I>
Shen, H. and Zhu, Z. (2008). Efficient mean estimation in log-normal linear models. Journal of Statistical Planning and Inference, 138: 552-567. <https://doi.org/10.1016/j.jspi.2006.10.016>
Longford, N. T. (2009). Inference with the lognormal distribution. Journal of Statistical Planning and Inference, 139: 2329-2340. <https://doi.org/10.1016/j.jspi.2008.10.015>
Fabrizi, E. and Trivisano, C. (2012). Bayesian estimation of log-normal means with finite quadratic expected loss. Bayesian Analysis, 7: 975-996. <https://doi.org/10.1214/12-BA733>
Gou, J. and Tamhane, A. C. (2017). Estimation of a parametric function associated with the lognormal distribution. Communications in Statistics - Theory and Methods 46: 8134-8154. <https://doi.org/10.1080/03610926.2016.1175628>
Zhang, F. and Gou, J. (2020). A unified framework for estimation in lognormal models. Technical Report.
1 2 3 4 5 6 7 8 9 | library(fuel)
# Unbiased Estimation (Finney, 1941)
fuel::lognormalmedian(data=c(1,4,6,7), estimator='unbiased')
# Longford's estimator, minimize the mean squared error (Longford, 2009)
fuel::lognormalmedian(data=c(1,4,6,7), estimator='l-ms')
# Gou and Tamhane's estimator, Rukhin type (Gou and Tamhane, 2017)
fuel::lognormalmedian(data=c(1,4,6,7), estimator='gt-r')
# Zhang and Gou's No.4 estimator (Zhang and Gou, 2020)
fuel::lognormalmedian(data=c(1,4,6,7), estimator='zg-4')
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