Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications

Hassan S Bakouch, Sanku Dey, Pedro Luiz Ramos, Francisco Louzada

Abstract


In this paper, we have considered different estimation methods of the unknown parameters of a binomial-exponential 2 distribution. First, we briefly describe different frequentist approaches such as the method of moments, modified moments, ordinary least-squares estimation, weighted
least-squares estimation, percentile, maximum product of spacings, Cramer-von Mises type minimum distance, Anderson-Darling and Right-tail Anderson-Darling, and compare them using extensive numerical simulations. We apply our proposed methodology to three real data sets related to the total monthly rainfall during April, May and September at Sao Carlos, Brazil.


Keywords


Binomial-exponential 2 , Maximum likelihood estimation, Cram\'{e}r-von-Mises type minimum distance estimators, Right-tail Anderson-Darling estimators

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References


M.R. Alkasasbeh & M.Z. Raqab. Estimation of the generalized logistic distribution parameters: Comparative study. Statistical Methodology, 6 (2009), 262–279.

T.W. Anderson & D.A. Darling. Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. The Annals of Mathematical Statistics, 23(2) (1952), 193–212.

T.W. Anderson & D.A. Darling. A test of goodness of fit. Journal of the American Statistical Associ- ation, 49 (1954), 765–769.

A. Asgharzadeh, H.S. Bakouch & M. Habibi. A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events. Journal of Applied Statistics, (2016), 1–20. Available online: http://dx.doi.org/10.1080/02664763.2016.1254729

A. Asgharzadeh, R. Rezaie & M. Abdi. Comparisons of methods of estimation for the half-logistic distribution. Selcuk Journal of Applied Mathematics, Special Issue (2011), 93–108.

H.S. Bakouch, M.A. Jazi, S. Nadarajah, A. Dolati & R. Roozegar. A lifetime model with increasing failure rate. Applied Mathematical Modelling, 38 (2014), 5392–5406.

D.D. Boos. Minimum distance estimators for location and goodness of fit. Journal of the American Statistical Association, 76 (1981), 663–670.

D.D. Boos. Minimum Anderson-Darling estimation. Communications in Statistics-Theory and Meth- ods, 11 (1982), 2747–2774.

R. Cheng & N. Amin. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society, Series B (Methodological), 45 (1983), 394–403.

R. Cheng & M. Stephens. A goodness-of-fit test using Moran’s statistic with estimated parameters. Biometrika, (1989), 385–392.

S. Dey, T. Dey & D. Kundu. Two-parameter Rayleigh distribution: different methods of estimation. American Journal of Mathematical and Management Sciences, 33 (2014), 55–74.

B. Efron & R.J. Tibshirani. An introduction to the bootstrap. CRC press, (1994), 1st Edition, 436 p.

R.D. Gupta & D. Kundu. Generalized exponential distribution: Different method of estimations. Journal of Statistical Computation and Simulation, 69 (2001), 315–337.

A. Henningsen & O. Toomet. maxlik: A package for maximum likelihood estimation in R. Computational Statistics, 26 (2011), 443–458. http://dx.doi.org/10.1007/s00180-010-0217-1.

J.H. Kao. Computer methods for estimating Weibull parameters in reliability studies. IRE Transactions on Reliability and Quality Control, 13 (1958), 15–22.

J.H. Kao. A graphical estimation of mixed Weibull parameters in life-testing of electron tubes. Technometrics, 1 (1959), 389–407.

F. Louzada, P.L. Ramos & G.S. Perdona. Different estimation procedures for the parameters of the extended exponential geometric distribution for medical data. Computational and Mathematical Methods in Medicine, 2016 (2016). Article ID 8727951, 12 pages. doi:10.1155/2016/8727951.

A. Luceno. Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estima- tors. Computational Statistics & Data Analysis, 51 (2006), 904–917.

J. Mazucheli, F. Louzada & M. Ghitany. Comparison of estimation methods for the parameters of the weighted Lindley distribution. Applied Mathematics and Computation, 220 (2013), 463–471.

S. Nadarajah & F. Haghighi. An extension of the exponential distribution. Statistics, 45 (2011), 543–558.

P. Ramos & F. Louzada. The generalized weighted Lindley distribution: Properties, estimation and applications. Cogent Mathematics, 3 (2016), 1–18.

B. Ranneby. The maximum spacing method. An estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 11 (1984), 93–112.

G.C. Rodrigues, F. Louzada & P.L. Ramos. Poisson-exponential distribution: different methods of estimation. Journal of Applied Statistics, (2016), pp. 1–17. Available online: http://dx.doi.org/ 10.1080/02664763.2016.1268571

V.K. Sharma, S.K. Singh, U. Singh & F. Merovci. The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communications in Statistics- Theory and Methods, 45 (2016), 5709–5729.

J.J. Swain, S. Venkatraman & J.R. Wilson. Least-squares estimation of distribution functions in John- son’s translation system. Journal of Statistical Computation and Simulation, 29 (1988), 271–297.

M. Teimouri, S.M. Hoseini & S. Nadarajah. Comparison of estimation methods for the Weibull dis- tribution. Statistics, 47 (2013), 93–109.




DOI: https://doi.org/10.5540/tema.2017.018.02.0233

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