The Beta-Weibull Distribution on the Lattice of Integers
DOI:
https://doi.org/10.5902/2179460X21864Keywords:
Beta-Weibull distribution, Discrete beta generalized exponential distributionAbstract
In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.
Downloads
References
BARRETO-SOUZA, W., SANTOS, A. H., CORDEIRO, G.M. (2010). The beta generalized exponential distribution. J. Stat. Comput. Simul.. 80(2): 159-172.
BIDRAM, H., BEHBOODIAN, J., TOWHIDI, M. (2013). The beta Weibull-geometric Distribution. J. Stat. Comput. Simul., 83(1): 52-67.
CASTELLARES, F., MONTENEGRO, L.C., CORDEIRO, G.M. (2013). The beta log-normal distribution. J. Stat. Comput. Simul., 83(2): 203-228.
CHAKRABORTY, S., CHAKRAVARTY, D. (2012). Discrete Gamma distributions: properties and parameter estimation. Comm. Stat.Theo. Meth., 41(18): 3301-3324.
CHAKRABORTY, S., CHAKRAVARTY, D. (2014). A Discrete Gumbel Distribution. arXiv: 1410.7568.
CORDEIRO, G.M., GOMES, A.E., SILVA, C.Q., ORTEGA, E.M.M. (2013a). The beta exponentiated Weibull distribution. J. Stat. Comput. Simul., 83(1): 114-138.
CORDEIRO, G.M., CRISTINO, C.T., HASHIMOTO, E.M., ORTEGA, E.M.M. (2013b). The beta generalized Rayleigh distribution with applications to lifetime data. Stat. Papers, 54: 133-161.
CORDEIRO, G.M., SILVA, G.O., ORTEGA, E.M.M. (2013c). The beta-Weibull geometric distribution, Statistics, 47: 817-834.
CORDEIRO, G.M., SIMAS, A.B., STOˇSI´C, B.D. (2011). Closed form expressions for moments of the beta Weibull distribution. Anais da Academia Brasileira de Ciˆencias, 83(2): 357-373.
CORDEIRO, G.M., LEMONTE, A.J. (2011a). The beta Laplace distribution. Stat. & Prob. Lett., 81: 973-982.
CORDEIRO, G.M., LEMONTE, A.J. (2011b). The beta-half-Cauchy distribution. J. Prob. Stat., 2011:1-18.
EUGENE, N., LEE, C. FAMOYE, F. (2002). Beta-normal distribution and its applications. Comm. Stat. Theo. Meth., 31: 497-512.
FERGUSON, T.S. (1996). A course in large sample theory. Chapman and Hall, London.
G´OMEZ-D´ENIZ E. (2010). Another generalization of the geometric distribution, Test, 19: 399-415.
G´OMEZ-D´ENIZ E., CALDERIN-OJEDA, E. (2011). The discrete Lindley distribution: properties and applications. J. Stat. Comput. Simul., 81(11): 1405-1416.
GUPTA, R.D., KUNDU, D. (1999). Generalized exponential distributions. Aust. NZ. J. Stat., 41(2): 173-188.
HUSSAIN, T., AHMAD, M. (2014). Discrete Inverse Rayleigh Distribution. Pak. J. Statist., 30(2): 203-222.
INUSAH, S., KOZUBOWSKI, T.J. (2006). A discrete analogue of the Laplace distribution. Statist. Plann.Infe., 136: 1090-1102.18
KEMP, A.W. (1992). HeineEuler extensions of the Poisson distribution. Commun. Stat. TheoryMethods,21(3): 571-588.
KEMP, A.W. (1997). Characterizations of discrete normal distribution. Statist. Plann. Inf., 63: 223-229.
KOTZ, S. LUMELSKII Y., PENSKY, M. (2003). The stress-strength model and its generalizations: Theory and Applications. Singapore: World Scientific 43, 44.
KOZUBOWSKI, T.J., INUSAH, S. (2006). A skew Laplace distribution on integers. AISM, 58: 555-571.
KRISHNA, H., PUNDIR, P.S. (2007). Discrete maxwell distribution. InterStat, November.
KRISHNA, H., PUNDIR, P.S. (2009). Discrete Burr and discrete Pareto distributions. Statist. Methodol., 6: 177-188.
LEE, H., CHA, J.H. (2015). On Two General Classes of Discrete Bivariate Distributions. The American Statistician, DOI: 10.1080/00031305.2015.1044564.
LEMONTE, A.J., CORDEIRO, G.M. (2013). An extended Lomax distribution. Statistics, 47(4): 800-816. bibitem Lisman, J.H.C., van Zuylen, M.C.A. (1972). Note on the generation of most probable frequency distributions. Statistica. Neerlan., 26(1): 19-23.
MAHMOUDI, E. (2011). The beta generalized Pareto distribution with application to lifetime data.Math. Comput. Simul., 81: 2414-2430.
MORAIS, A.L., Cordeiro, G.M., Audrey, H.M.A. (2013). The beta generalized logistic distribution. Brazilian J. Prob. Stat., 27: 185-200.
MUDHOLKAR, G.S, SRIVASTAVA, D.K., FREIMER, M. (1995). The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. Technometrics, 37: 436-445.
NADARAJAH, S., KOTZ, S. (2006). The beta exponential distribution. Reli. Engin. Sys. Saf., 91: 689-697.
NAKAGAWA, T., OSAKI, S. (1975). The discrete Weibull distribution. IEEE Transact. Reliab., 24(5): 300-301.
NEKOUKHOU, V., ALAMATSAZ, M.H., BIDRAM, H. (2013). Discrete generalized exponential distribution of a second type.
Statistics, 47(4): 876-887.
NEKOUKHOU, V., ALAMATSAZ, M.H. BIDRAM, H. AGHAJANI, A.H. (2015). Discerte beta exponential distribution. Commun. Stat. Theory-Methods, 44: 2079-2091.
NEKOUKHOU, V., BIDRAM, H. (2015a). A new four-parameter discrete distribution with bathtub and unimodal failur rate. J. Applied Statistics, 42(12): 2654-2670.
NEKOUKHOU, V., BIDRAM, H. (2015b). The exponentiated discrete Weibull distribution. SORT, 39(1): 127-146.
NEKOUKHOU, V. (2015). The Beta-Rayleigh Distribution on the Lattice of Integers. J. Statistical research of Iran, 12: 205224.
RAUE, A., KREUTZ, C., MAIWALD, T., BACHMANN, J., SCHILLING, M., KLINGMLLER, U., TIMMER, J. (2009). Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics, 25(15), 1923-1929.
ROY, D. (2003). The discrete normal distribution. Comm. Stat.Theo. Meth., 32(10): 1871-1883.
ROY, D. (2004). Discrete Rayleigh distribution,. IEEE Trans. Reliab, 53: 255-260.
SILVA, G.O., ORTEGA, E.M.M., CORDEIRO, G.M. (2010). The beta modified Weibull distribution. Life. data Anal., 16: 409-430.
SINGLA, N., JAIN, K., SHARMA, S.K. (2012). The beta generalized Weibull distribution: Properties and applications. Reli. Engin. Sys. Saf., 102: 5-15.
STEUTEL, F.W., VAN HARN, K. (2004). Infinite Divisibility of Probability Distributions on the Real Line. New York: Marcel Dekker.
Downloads
Published
How to Cite
Issue
Section
License
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
In particular,
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.
