Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics

Diana Bílková

doi:doi:10.11648/j.ajam.20140202.11

| Peer-Reviewed

Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics

Diana Bílková

Published in American Journal of Applied Mathematics (Volume 2, Issue 2)

Received: 24 March 2014 Accepted: 10 April 2014 Published: 20 April 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Application of the method of moments for the parametric distribution is common in the construction of a suitable parametric distribution. However, moment method of parameter estimation does not produce good results. An alternative approach when constructing an appropriate parametric distribution for the considered data file is to use the so-called order statistics. This paper deals with the use of order statistics as the methods of L-moments and TL-moments of parameter estimation. L-moments have some theoretical advantages over conventional moments. L-moments have been introduced as a robust alternative to classical moments of probability distributions. However, L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of L-moments and TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. There are method of TL-moments, method of L-moments and maximum likelihood method in combination with Cohen’s method. A total of 328 wage distribution has been the subject of research

Published in	American Journal of Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ajam.20140202.11
Page(s)	36-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Order Statistics, L-Moments, Tl-Moments, Maximum Likelihood Method, Probability Density Function, Distribution Function, Quantile Function, Lognormal Curves, Model of Wage Distribution

References

[1]	J. R. M. Hosking, “L-moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics,” Journal of the Royal Statistical Society (Series B), 1990, Vol. 52, No. 1, pp. 105–124. ISSN 1467-9868.
[2]	J. Kyselý and J. Picek, “Regional Growth Curves and Improved Design value Estimates of Extreme Precipitation Events in the Czech Republic,” Climate research, 2007, Vol. 33, pp. 243−255. ISSN: 0936-577X.
[3]	T. J. Ulrych, D. R.Velis, A. D. Woodbury and M. D. Sacchi, “L-moments and C-moments,” Stoch. Environ. Res. Risk Asses, 2000, Vol. 14, pp. 50–68. ISSN 1436-3240.
[4]	K. Adamowski, “Regional Analysis of Annual Maximum and Partial Duration Flood Data by Nonparametric and L-moment Methods,” Journal of Hydrology, 2000, Vol. 229, pp. 219−231. ISSN 0022-1694.
[5]	D. Bílková, “Modelling of Wage Distributions Using the Method of L-Moments,” Paper presented at AMSE – Applications of Mathematics and Statistics in Economy held on 25–28 August 2010, Demänovská Dolina, pp. 16–30. ISBN 978-80-89438-02-0.
[6]	D. Bílková, “Use of the L-Moments Method in Modeling the Wage Distribution,” Paper presented at Aplimat held on 01–04 February 2011, Bratislava, pp. 1471–1481. ISBN 978-80-89313-52-5.
[7]	D. Bílková, “L-Moments and Their Use in Modeling the Distribution of Income and Wage,” Paper presented at ISI held on 21–26 August 2011, Dublin, flashdisk, pp. 1–6.
[8]	D. Bílková, “Modeling of Income and Wage Distribution Using the Method of L-Moments of Parameter Estimation,” Paper presented at International Days of Statistics and Economics at VŠE held on 22–23 September 2011, Prague, pp. 1–10. ISBN 978-80-86175-72-0.
[9]	D. Bílková, “Three-Parametric Lognormal Distribution and Estimating Its parameters Using the Method of L-Moments,” Paper presented at RELIK – Reprodukce lidského kapitálu held on 05–06 December 2011, Prague, CD. ISBN 978-80-86175-75-1.
[10]	D. Bílková, “Estimating Parameters of Lognormal Distribution Using the Method of L-Moments,” Research Journal of Economics, Business and ICT, 2011, Vol. 4, No. 1, pp. 4–9. ISSN 2045-3345.
[11]	D. Bílková, “Modelling of Wage and Income Distributions Using the Method of L-Moments,” Journal of Mathematics and System Science, 2012, Vol. 2, No. 1, pp. 13–19. ISSN 2159-5291.
[12]	D. Bílková and I. Malá, I. “Application of the L-Moment Method when Modelling the Income Distribution in the Czech Republic,” Austrian Journal of Statistics, 2012, Vol. 41, No. 2, pp. 125–132. ISSN: 1026-597X.
[13]	E. A. H. Elamir and A. H. Seheult, “Trimmed L-moments,” Computational Statististics & Data Analysis, 2003, Vol. 43, No. 3, pp. 299–314. ISSN: 0167-9473.
[14]	D. Bílková, “Lognormal Distribution and Using L-Moment Method for Estimating Its Parameters,” International Journal of Mathematical Models and Methods in Applied Sciences [online], 2012, Vol. 6, No. 1, pp. 30–44. ISSN 1998-0140. URL: http://www.naun.org/journals/m3as/17-079.pdf.
[15]	D. Bílková, “Lognormal Distribution Parameter Estimating Using L-Moments,” Journal of Mathematics and Technology, 2012, Vol. 3, No. 1, pp. 33–51. ISSN: 2078-0257.
[16]	N. L. Johnson, S. Kotz and N. Balakrishnan, “Continuous Univariate Distributions”, Wiley-Interscience, 1994. 756 p. ISBN 0-471-58495-9.
[17]	C. Kleiber and S. Kotz , „Statistical Size Distributions in Economics and Actuarial Sciences“, Wiley-Interscience, 2003. 332 p. ISBN 0-471-15064-9.
[18]	T. Löster and J. Langhamrová, „Analysis of Long-Term Unemployment in the Czech Republic“, Proceedings Conference International Days of Statististics and Economics at VŠE 2011, Prague, Czech Republic, 22.09.2011–23.09.2011, pp. 228–234, CD. ISBN 978-80-86175-72-0.
[19]	L. Marek, “Wage development in the Czech Republic for the past 16 years,” Paper presented at AIESA – Budovanie společnosti založenej na vedomostiach held on 10–11 November 2011, Bratislava, pp. 1–7. ISBN 978-80-225-3312-6.
[20]	L. Marek and M. Vrabec, “Mixture Normal Density Functions as a Model Wage Distribution,” Paper presented at Economic, Marketing and Management held on 19–20 January 2013, Dubai, pp. 69–74. ISBN 978-981-07-5039-8. ISSN 2010-4626.
[21]	M. H. Atyeh and W. Al-Rashed, „Testing the Existence of Integration; Kuwait and Jordan Financial Markets,“ International Journal of Economics, Finance and Management Sciences, 2013, Vol. 1 No. 2, pp. 89–94. doi: 10.11648/j.ijefm.20130102.14

Cite This Article

Plain Text BibTeX RIS

APA Style

Diana Bílková. (2014). Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. American Journal of Applied Mathematics, 2(2), 36-53. https://doi.org/10.11648/j.ajam.20140202.11

Copy | Download

ACS Style

Diana Bílková. Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. Am. J. Appl. Math. 2014, 2(2), 36-53. doi: 10.11648/j.ajam.20140202.11

Copy | Download

AMA Style

Diana Bílková. Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. Am J Appl Math. 2014;2(2):36-53. doi: 10.11648/j.ajam.20140202.11

Copy | Download

@article{10.11648/j.ajam.20140202.11,
  author = {Diana Bílková},
  title = {Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {36-53},
  doi = {10.11648/j.ajam.20140202.11},
  url = {https://doi.org/10.11648/j.ajam.20140202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140202.11},
  abstract = {Application of the method of moments for the parametric distribution is common in the construction of a suitable parametric distribution. However, moment method of parameter estimation does not produce good results. An alternative approach when constructing an appropriate parametric distribution for the considered data file is to use the so-called order statistics. This paper deals with the use of order statistics as the methods of L-moments and TL-moments of parameter estimation. L-moments have some theoretical advantages over conventional moments. L-moments have been introduced as a robust alternative to classical moments of probability distributions. However, L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of L-moments and TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. There are method of TL-moments, method of L-moments and maximum likelihood method in combination with Cohen’s method. A total of 328 wage distribution has been the subject of research},
 year = {2014}
}

Copy | Download

TY - JOUR
T1 - Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics
AU - Diana Bílková
Y1 - 2014/04/20
PY - 2014
N1 - https://doi.org/10.11648/j.ajam.20140202.11
DO - 10.11648/j.ajam.20140202.11
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 36
EP - 53
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.20140202.11
AB - Application of the method of moments for the parametric distribution is common in the construction of a suitable parametric distribution. However, moment method of parameter estimation does not produce good results. An alternative approach when constructing an appropriate parametric distribution for the considered data file is to use the so-called order statistics. This paper deals with the use of order statistics as the methods of L-moments and TL-moments of parameter estimation. L-moments have some theoretical advantages over conventional moments. L-moments have been introduced as a robust alternative to classical moments of probability distributions. However, L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of L-moments and TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. There are method of TL-moments, method of L-moments and maximum likelihood method in combination with Cohen’s method. A total of 328 wage distribution has been the subject of research
VL - 2
IS - 2
ER -

Copy | Download

Author Information

Diana Bílková

Department of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, Prague, Czech Republic; Department of Informatics and Mathematics, Faculty of Economic Studies, University of Finance and Administration, Czech Republic

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Diana Bílková. (2014). Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. American Journal of Applied Mathematics, 2(2), 36-53. https://doi.org/10.11648/j.ajam.20140202.11

Copy | Download

ACS Style

Diana Bílková. Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. Am. J. Appl. Math. 2014, 2(2), 36-53. doi: 10.11648/j.ajam.20140202.11

Copy | Download

AMA Style

Diana Bílková. Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics. Am J Appl Math. 2014;2(2):36-53. doi: 10.11648/j.ajam.20140202.11

Copy | Download

@article{10.11648/j.ajam.20140202.11,
  author = {Diana Bílková},
  title = {Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {36-53},
  doi = {10.11648/j.ajam.20140202.11},
  url = {https://doi.org/10.11648/j.ajam.20140202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140202.11},
  abstract = {Application of the method of moments for the parametric distribution is common in the construction of a suitable parametric distribution. However, moment method of parameter estimation does not produce good results. An alternative approach when constructing an appropriate parametric distribution for the considered data file is to use the so-called order statistics. This paper deals with the use of order statistics as the methods of L-moments and TL-moments of parameter estimation. L-moments have some theoretical advantages over conventional moments. L-moments have been introduced as a robust alternative to classical moments of probability distributions. However, L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of L-moments and TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. There are method of TL-moments, method of L-moments and maximum likelihood method in combination with Cohen’s method. A total of 328 wage distribution has been the subject of research},
 year = {2014}
}

Copy | Download