Estimating Cumulative Distribution Functions with Maximum Likelihood to Sample Data Sets of a Sea Floater Model

- Journal title : Journal of Navigation and Port Research
- Volume 37, Issue 5, 2013, pp.453-461
- Publisher : Korean Institute of Navigation and Port Research
- DOI : 10.5394/KINPR.2013.37.5.453

Title & Authors

Estimating Cumulative Distribution Functions with Maximum Likelihood to Sample Data Sets of a Sea Floater Model

Yim, Jeong-Bin; Yang, Won-Jae;

Yim, Jeong-Bin; Yang, Won-Jae;

Abstract

This paper describes evaluation procedures and experimental results for the estimation of Cumulative Distribution Functions (CDF) giving best-fit to the sample data in the Probability based risk Evaluation Techniques (PET) which is to assess the risks of a small-sized sea floater. The CDF in the PET is to provide the reference values of risk acceptance criteria which are to evaluate the risk level of the floater and, it can be estimated from sample data sets of motion response functions such as Roll, Pitch and Heave in the floater model. Using Maximum Likelihood Estimates and with the eight kinds of regulated distribution functions, the evaluation tests for the CDF having maximum likelihood to the sample data are carried out in this work. Throughout goodness-of-fit tests to the distribution functions, it is shown that the Beta distribution is best-fit to the Roll and Pitch sample data with smallest averaged probability errors of 0.024 and 0.022, respectively and, Gamma distribution is best-fit to the Heave sample data with smallest of 0.027. The proposed method in this paper can be expected to adopt in various application areas estimating best-fit distributions to the sample data.

Keywords

sea floater;risk evaluation;risk acceptance criteria;cumulative distribution function;maximum likelihood estimates;

Language

Korean

Cited by

References

1.

Breheny Patrick(2013), Introduction to the empirical distribution function(STA 621): Nonparametric Statistics, white paper, http://web.as.uky.edu/statistics/users/pbreheny/621/F10/notes/8-26.pdf.

2.

Charles R. Farrar, Scott W. Doebling and David A. Nix(2001), "Vibration-based structural damage identification," Philosophical Transactions of the Royal Society A, Londo, Vol. 359, pp. 131-149.

3.

David Vose(2010), Fitting Distributions to Data and why you are probably doing it wrong, white paper, http://www.vosesoftware.com/whitepapers/Fitting%20distributions%20to%20data.pdf.

4.

Joel Azose(2013), On the Gamma Function and Its Applications, white paper, http://www.math.washington.edu/-morrow/336_10/papers/joel.pdf.

5.

Jose Miguel Simon Donaire(2009), Sea Transport Analysis of Upright Wind Turbines, Master Thesis(MEK-FM-EP-2009-14), Technical University of Denmark.

6.

Jun Chang Hyun and Yoo Chul Sang(2012), "Application of the Beta Distribution for the Temporal Quantification of Storm Events," Journal of Korea Water Resources Association, Vol. 45, Issue 6, pp. 531-544.

7.

Kim Jin Ho, Kim Hyeong Seok and Cho Sung Ho(2013), "A Ranging Algorithm for IR-UWB in Multi-Path Environment Using Gamma Distribution," The Journal of Korea Information and Communications Society, Vol. 38B, No. 2, pp. 146-153.

8.

Lee J. T. and Oh H. J(1996), "Approximation Equation of Cumulative Distribution Function on the Normal Distribution," Journal of the Korea Society of Mathematical Education, Series A, Vol. 35, No. 1, pp. 57-59, http://www.mathnet.or.kr/mathnet/kms_tex/982256.pdf.

9.

Lu Kung-Chun, Loh Chin-Hsiung, Yang Y. S., Jerome P. Lynch and Kincho H. Law(2008), "Real-Time Structural Damage Detection using Wireless Sensing and Monitoring System," Smart Structures and Systems, TechnoPress, Vol. 4(6), pp. 759-778.

10.

MATLAB(2008a), Programming, MATLAB Version 7.6 (R2008a)

11.

MATLAB(2008b), Statistical Toolbox : Maximum likelihood estimation, MATLAB Version 7.6 (R2008a).

12.

MATLAB(2008c), Statistical Toolbox : Empirical Cumulative Distribution Function, MATLAB Version 7.6 (R2008a).

13.

MathWorks(2013), Statistical Toolbox Distribution Functions, http://www.mathworks.co.kr/kr/help/stats/statistics-toolbox-distribution-functions.html.

14.

Plancade Sandra(2013), Adaptive estimation of the conditional cumulative distribution function from current status data, Institute of Community Medicine, white paper, University of Tromso, Norway, pp. 1-42, http://sandraplancade.perso.math.cnrs.fr/cens-int.pdf.

15.

R-forge project(2013), Handbook on probability distributions, white paper, R-forge distributions Core Team, University Year 2009-2010, pp. 1-167, https://r-forge.r-project.org/scm/viewvc.php/*checkout*/pkg/inst/doc/probdistr-main.pdf.

16.

Riddhi D.(2013), Beta Function and its Applications, white paper, Department of Physics and Astronomy, The University of Tennessee, USA, pp. 1-4, http://sces.phys.utk.edu/-moreo/mm08/Riddi.pdf.

17.

Staub Linda and Gekenidis Alexandros(2011), Seminar in Statistics: Survival Analysis Chapter 2, white paper, pp. 1-39, http://stat.ethz.ch/education/semesters/ss2011/seminar/contents/presentation_2.pdf.

18.

Wikipedia(2013a), Tutorial for Probability distribution, http://en.wikipedia.org/wiki/Probability_distribution.

19.

Wikipedia(2013b), Tutorial for Arg max, http://en.wikipedia.org/wiki/Arg_max.

20.

Wikipedia(2013c), Tutorial for Maximum Likelihood, https://en.wikipedia.org/wiki/Maximum_likelihood.