Point estimation methods for the three-parameter lognormal distribution are investigated and compared. The lognormal distribution is required in many topical areas, but so far there have been no comparative studies of the various estimation methods. We show that despite the large number of traditional estimation methods, the lognormal distribution requires special methods. We accordingly consider specializations of the main parameter estimation approaches, including the actively developing distance minimization methods. Their accuracy and speed are compared on simulated data. We show that specialized parameterestimation methods may outperform the highly popular maximum likelihood method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. A. Gorelov, A. I. Maysuradze, and A. N. Salnikov, “Delay structure mining in computing cluster,” CEUR Workshop Proceedings, 1482, 546–551, M. Jeusfeld c/o Redaktion Sun SITE, Informatik V, RWTH, Aachen, Germany (2015).
A. Corlett, D. I. Pullin, and S. Sargood, “Statistics of one-way internet packet delays,” Proceedings of the 53rd Internet Engineering Task Force (2002).
M. Karakas, Determination of Network Delay Distribution over the Internet, Master Thesis, The Middle East Technical University (2003).
A. Mukherjee, “On the dynamics and significance of low frequency components of internet load,” Internetworking: Research and Experience, 5, 163–205 (1994).
S. A. Aivazyan and V. S. Mkhitaryan, Applied Statistics. Foundations of Econometrics, Vol. 1: Probability Theory and Applied Statistics [in Russian], Yuniti-Dana, Moscow (2001).
A. I. Kobzar’, Applies Mathematical Statistics [in Russian], Fizmatlit, Moscow (2006).
N. L. Johnson, S. B. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Wiley, New York (1994).
A. C. Cohen and B. J. Whitten, “Estimation in the three-parameter lognormal distribution,” J. Amer. Stat. Association, 75(370), 399–404 (1980).
A. C. Cohen and B. J. Whitten, Parameter Estimation in Reliability and Life Span Models, Marcel Dekker (1988).
B. M. Hill, “The three-parameter lognormal distribution and bayesian analysis of a point-source epidemic,” J. Amer. Stat. Association, 58(301), 72–84 (1963).
F. Calitz, “maximum likelihood estimation of the parameters of the three-parameter lognormal distribution — a reconsideration,” Australian J. Statistics, 15(3), 185–190 (1973).
D. Bilkova, “Three-parametric lognormal distribution and estimating its parameters using the method of L-moments,” RELIK — Reprodukce Lidskeho Kapitalu (2011).
J. R. M. Hosking, “L-moments: Analysis and estimation of distributions using linear combinations of order statistics,” J. Royal Stat. Soc. Series B (Methodological), 52(1), 105–124.
A. Basu, H. Shioya, and C. Park, Statistical Inference: The Minimum Distance Approach, Taylor & Francis (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 60, 2019, pp. 79–89.
Rights and permissions
About this article
Cite this article
Kozlov, V.D., Maysuradze, A.I. Parameter Estimation in a Three-Parameter Lognormal Distribution. Comput Math Model 30, 302–310 (2019). https://doi.org/10.1007/s10598-019-09456-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-019-09456-9