Comparison of different estimation methods for extreme value distribution

References

• I.B. Abdul-Moniem, L-moments TL-moments estimation for the exponential distribution. Far East J. Theor. Stat. 23 (2007), pp. 51.
   Google Scholar
• A.C. Aitken, On least squares and linear combination of observations. Proc. R. Soc. Edinb. 55 (1936), pp. 42–48.
   Google Scholar
• D. Aydin, Estimation of the lower and upper quantiles of Gumbel distribution: An application to wind speed data. Appl. Ecol. Environ. Res. 16 (2016), pp. 1–15.
   Web of Science ®Google Scholar
• D. Aydin and B. Şenoğlu, Monte Carlo comparison of the parameter estimation methods for the two-parameter Gumbel distribution. J. Mod. Appl. Stat. Methods 14 (2015), pp. 123–140.
   Web of Science ®Google Scholar
• H. Aydoğdu and Ö Altındağ, Computation of the mean value and variance functions in geometric process. J. Stat. Comput. Simul. 86 (2016), pp. 986–995.
   Web of Science ®Google Scholar
• M.H. Chen and Q.M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals. J. Comput. Graph. Stat. 8 (1999), pp. 69–92.
   Web of Science ®Google Scholar
• Y.C. Chen and C.L. Chiu, A fast method of flood discharge estimation. Hydrol. Processes 18 (2004), pp. 1671–1684.
   Web of Science ®Google Scholar
• K. Cooray, Generalized Gumbel distribution. J. Appl. Stat. 37 (2010), pp. 171–179.
   Web of Science ®Google Scholar
• G.M. Cordeiro, S. Nadarajah, and E.M. Ortega, The Kumaraswamy Gumbel distribution. Stat. Methods Appt. 21 (2012), pp. 139–168.
   Web of Science ®Google Scholar
• H. David and H.N. Nagaraja, Order Statistics, Encyclopedia of Statistical Sciences, New Jersey, 2004.
   Google Scholar
• H. Demirhan and Z. Kalaylioglu, On the generalized multivariate Gumbel distribution. Stat. Probab. Lett. 103 (2015), pp. 93–99.
   Web of Science ®Google Scholar
• S. Dey, S. Ali, and C. Park, Weighted exponential distribution: Properties and different methods of estimation. J. Stat. Comput. Simul. 85 (2015), pp. 3641–3661.
   Web of Science ®Google Scholar
• S. Dey, J. Mazucheli, and S. Nadarajah, Kumaraswamy distribution: Different methods of estimation. Comput. Appl. Math. 37 (2018), pp. 2094–2111.
   Web of Science ®Google Scholar
• S. Dey, C. Zhang, A. Asgharzadeh, and M. Ghorbannezhad, Comparisons of methods of estimation for the NH distribution. Ann. Data Sci. 4 (2017), pp. 441–455.
   Google Scholar
• D. Dietrich and J. Hüsler, Minimum distance estimators in extreme value distributions. Commun. Stat. Theory Methods 25 (1996), pp. 695–703.
   Web of Science ®Google Scholar
• E.A. Elamir and A.H. Seheult, Trimmed- L-moments. Comput. Stat. Data Anal. 43 (2003), pp. 299–314.
   Web of Science ®Google Scholar
• M. Engelhardt and L.J. Bain, Simplifed statistical procedures for the Weibull or extreme value distributions. Techeometrics 19 (1977), pp. 323–331.
   Web of Science ®Google Scholar
• M.N.P. Fard and B. Holmquist, First moments approximations for order statistics from the extreme value distribution. Stat. Methodol. 4 (2007), pp. 196–203.
   Google Scholar
• C.F. Gauss, Least Squares Method for the Combinations of Observations (Translated by J. Bertrand 1955), Mallet-Bachelier, Paris, 1810.
   Google Scholar
• Y.M. Gómez, H. Bolfarine, and H.W. Gómez, Gumbel distribution with heavy tails and applications to environmental data. Math. Comput. Simul. 157 (2019), pp. 115–129.
   Web of Science ®Google Scholar
• E.J. Gumbel, The return period of flood follows. Ann. Math. Stat. 12 (1941), pp. 163–190.
   Google Scholar
• J. Gupta, M. Garg, and M. Gupta, The Lomax-Gumbel distribution. Palest. J. Math. 5 (2016), pp. 35–42.
   Google Scholar
• R.D. Gupta and D. Kundu, Generalized exponential distribution: Different method of estimations. J. Stat. Comput. Simul. 69 (2007), pp. 315–337.
   Web of Science ®Google Scholar
• W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970), pp. 97–109.
   Web of Science ®Google Scholar
• J.R. Hosking, L-moments: Analysis and estimation of distributions using linear combinations of order statistics. J. R. Stat. Soc. B (Methodol.) 52 (1990), pp. 105–124.
   Web of Science ®Google Scholar
• N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Houghton Mifflin, Boston, MA, 1970.
   Google Scholar
• J.H. Kao, Computer methods for estimating Weibull parameters in reliability studies. IRE Trans. IRE Reliab. Qual. Control 13 (1958), pp. 15–22.
   Google Scholar
• S. Kotz and S. Nadarajah, Extreme Value Distributions: Theory and Applications, World Scientific, London, 2000.
   Google Scholar
• K. Krishnamoorthy, Handbook of Statistical Distributions with Applications, CRC, Boca Raton, 2006.
   Google Scholar
• K. Kumar, Classical and Bayesian estimation in log-logistic distribution under random censoring. Int. J. Syst. Assur. Eng. Manag. 9 (2018), pp. 440–451.
   Web of Science ®Google Scholar
• D. Kundu and M.Z. Ragab, Generalized Rayleigh distribution: Different method of estimations. Comput. Stat. Data Anal. 49 (2005), pp. 187–200.
   Web of Science ®Google Scholar
• B.H. Lee, D.J. Ahn, H.G. Kim, and Y.C. Ha, An estimation of the extreme wind speed using the Korea wind map. Renew. Energy 42 (2012), pp. 44–10.
   Web of Science ®Google Scholar
• A. Legendre, New Methods for the Determination of Orbits of Comets Courcier, Paris, 1805.
   Google Scholar
• J. Lieblien, On the exact evaluation of the variances and covariances of order statistics in samples from the extreme-value distribution. Ann. Math. Stat. 24 (1953), pp. 282–287.
   Google Scholar
• D.V. Lindley, Approximate Bayesian methods. Trab. Estad. Investig. Oper. 31 (1980), pp. 223–245.
   Google Scholar
• E.H. Lloyd, Least-squares estimation of location and scale parameters using order statistics. Biometrika 39 (1952), pp. 88–95.
   Web of Science ®Google Scholar
• S. Mahdi and M. Cenac, Estimating parameters of Gumbel distribution using the methods moments, probability weighted moments and maximum likelihood. Rev. Mat. Teor. Apl. 12 (2005), pp. 151–156.
   Google Scholar
• N.R. Mann, N.D. Singpurwalla, and R.E. Schafer, Methods for Statistical Analysis of Reliability and Life Data, John Wiley & Sons, New Jersey, 1974.
   Google Scholar
• J. Mazucheli, F. Louzada, and M.E. Ghitany, Comparison of estimation methods for the parameters of the weighted Lindley distribution. Appl. Math. Comput. 220 (2013), pp. 463–471.
   Web of Science ®Google Scholar
• N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys. 21 (1953), pp. 1087–1092.
   Web of Science ®Google Scholar
• M.A. Mousa, Z.F. Jaheen, and A.A. Ahmad, Bayesian estimation, prediction and characterization for the Gumbel model based on records. Stat. J. Theor. Appl. Stat. 36 (2002), pp. 65–74.
   Google Scholar
• G.S. Mudholkar and A.D. Hutson, LQ-moments: Analogs of L-moments. J. Stat. Plan. Inference. 71 (1998), pp. 191–208.
   Web of Science ®Google Scholar
• S. Nadarajah, The exponentiated Gumbel distribution with climate application. Environmetrics Off. J. Int. Environmetrics Soc. 17 (2006), pp. 13–23.
   Web of Science ®Google Scholar
• S. Nadarajah and S. Kotz, The beta Gumbel distribution. Math. Probl. Eng. 2004 (2004), pp. 323–332.
   Web of Science ®Google Scholar
• L.R. Pericchi and I. Rodríguez-Iturbe, On the Statistical Analysis of Floods, A Celebration of Statistics Springer, New York, 1985, pp. 511–541.
   Google Scholar
• P.L. Ramos, F. Louzada, E. Ramos, and S. Dey, The Fréchet distribution: Estimation and application – an overview. J. Stat. Manag. Syst. 23 (2019), pp. 1–30.
   Google Scholar
• A.F. Smith and G.O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Stat. Soc. B (Methodol.) 55 (1993), pp. 3–23.
   Web of Science ®Google Scholar
• J.J. Swain, S. Venkatraman, and J.R. Wilson, Least-squares estimation of distribution function in Johnson’s translation system. J. Stat. Comput. Simul. 29 (1988), pp. 271–297.
   Google Scholar
• M. Teimouri, S.M. Hoseini, and S. Nadarajah, Comparison of estimation methods for the Weibull distribution. Statistics 47 (2013), pp. 93–109.
   Web of Science ®Google Scholar
• M. Uludağ and H. Turoğlu, Possible hydrographic effects of climate change on lower part of transboundary meric River basin (Turkey). Trak. Univ. J. Nat. Sci. 14 (2013), pp. 77–85.
   Google Scholar
• J.S. White, The moments of log-Weibull order statistics. Techometrics 11 (1969), pp. 373–386.
   Web of Science ®Google Scholar