Record Values from the Gumbel and q- Gumbel Distributions with Applications
Keywords:
Maximum likelihood estimates, best linear unbiased estimators, best linear invariant estimators, Akaike information criterion, corrected Akaike information criterionAbstract
In the present study we investigate the problem of estimating the inherent parameters of the Gumbel and q-Gumbel distributions using record breaking data. We presented the coefficients of the best linear unbiased estimators (BLUE) for location and scale parameters of the Gumbel and q-Gumbel distributions. Finally, the usefulness of our result is illustrated using a simulation study.
References
Ahsanullah M. Linear prediction of record values for the two parameter exponential distribution. Ann
I Stat Math. 1980; 32: 363-368.
Akaike H. A new look at the statistical model identification: IEEE T Automat Contr. 1974; 19(6):716-
Chandler KM. The distribution and frequency of record values. J Roy Stat Soc B Met. 1952; 14:
-228.
Coles SG. An Introduction to Statistical Modeling of Extreme Values. New York: Springer; 2001.
Feller W. An Introduction to Probability Theory and its Application. New York: John Wily 7 sons,
Inc; 1965.
Gulati S and Padgett WJ. Parametric and Nonparametric Inference from Record-Breaking Data. New
York: Springer; 2003.
Gumbel EJ. Statistics of Extremes. New York: Columbia University Press; 1958.
Haan L, Ferreira A. Extreme Value Theory (An Introduction), New York: Springer; 2006.
Hosking JRM, Wallis JR, and Wood EF. Estimation of the generalized extreme value distribution by
the method of probability weighted moments. Technometrics. 1985; 27: 251- 261.
Jose KK and Naik SR. On the q-Weibull distribution and its applications, Commun Stat Theory. 2009;
: 912-926.
Kotz S and Nadarajah S. Extreme Value Distributions: Theory and App. London: Imperial College
Press; 2000.
Llyod EH. Least squares estimation of location and scale parameters using order statistics.
Biometrika. 1952; 39: 88-95.
Luo CW, Zhu J. Estimates of the parameters of the Gumbel distribution and their application to
analysis of water level data. Chinese J Appl Probab Statist. 2005; 21(2): 169-175.
Mathai AM and Haubold HJ. Pathway model, superstatistics, Tsallis statistics and a generalized measure of entropy. Physica A. 2007; 375: 110-122.
Mathai AM and Provost SB. On q-Logistic and related models: IEEE T Reliab. 2006; 55: 237-344.
Mathai AN and Provost SB. The q-extended inverse Gaussian distribution. J Probab Stat Sci. 2011;
: 1-20.
Mbah KA and Ahsanullah M. Some characterizations of the power function distribution based on
lower generalized order statistics. Pak J Stat. 2007; 23: 139-146.
Mbah KA and Tsokos PC. On the theory and application of Gumbel distribution using records. Fifth
International Conference on Dynamic Sys. and Apps; 2007 May 30 - June 2; Morehouse College, Atlanta, Georgia, USA.
Murat T and David H. Unbiased estimates of the Weibull parameters by the linear regression method.
J Mater Sci. 2008; 43: 1914-1919.
Nigm EM. Record values from inverse Weibull distribution and associated inference. J Appl Stat.
; 16: 103-114.
Provost BS. On the q-generalized extreme value distribution: Revstat Stat J. 2018; 15(1): 45-70.
Raul G, Javier F, Lina M and Gerardo S. Statistical inference for the Weibull distribution based on
δ-record data. Symmetry. 2019; 12(1): 1-24.
Samaniego FJ and Whitaker LR. On Estimating population characteristics from record-breaking observations. I. parametric results. Nav Res Logist Q. 1986; 33: 531-543.
Wilk G and Wlodarczyk Z. Interpretation of the nonextensivity parameter q in some applications of
Tsallis statistics and Levy Distributions. Phys Rev Lett. 2000; 84: 2770-2773.
Wilk G and Wlodarczyk Z. Non-exponential decays and nonextensivity: Physica A. 2001; 290: 55-
Zeinhum J. Empirical Bayes inference for generalized exponential distribution based on records.
Commun Stat Theory. 2004; 33: 1851-1861.
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