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

Authors

  • Hassan S Bakouch King Abdulaziz University, Jeddah
  • Sanku Dey Department of Statistics, St. Anthony's College, Shillong, Meghalaya,
  • Pedro Luiz Ramos Institute of Mathematical Science and Computing http://orcid.org/0000-0002-5387-2457
  • Francisco Louzada Institute of Mathematical Science and Computing

DOI:

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

Keywords:

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

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.

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.

Downloads

Additional Files

Published

2017-08-24

How to Cite

Bakouch, H. S., Dey, S., Ramos, P. L., & Louzada, F. (2017). Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications. Trends in Computational and Applied Mathematics, 18(2), 233. https://doi.org/10.5540/tema.2017.018.02.0233

Issue

Vol. 18 No. 2 (2017)

Section

Original Article

License

Copyright

Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.

Intellectual Property and Terms of Use

The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.

The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.