Univariate and bivariate extensions of the generalized exponential distributions
-
Vahid Nekoukhou
,
Ashkan Khalifeh
Abstract
The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.
Acknowledgement
The authors sincerely thank the anonymous referees for their valuable comments that led to improvement of the paper and also special thanks to the Editor for all his/her considerations in this paper.
Communicated by Gejza Wimmer
References
[1] Adamidis, K.—Loukas, S.: A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), 35–42.10.1016/S0167-7152(98)00012-1Suche in Google Scholar
[2] Adamidis, K.—Dimitrakopoulou, T.—Loukas, S.: On an extension of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), 259–269.10.1016/j.spl.2005.03.013Suche in Google Scholar
[3] Barreto-Souza, W.—de Morais, A. L.—Cordeiro, G. M.: The Weibull-geometric distribution, J. Stat. Comput. Simul. 81(5) (2011), 645–657.10.1080/00949650903436554Suche in Google Scholar
[4] Bidram, H.—Behboodian, J.—Towhidi, M.: A new generalized exponential geometric distribution, Comm. Statist. Theory Methods 42 (2013), 528–542.10.1080/03610926.2011.579703Suche in Google Scholar
[5] Dempster, A. P.—Laird, N. M.—Rubin, D. B.: Maximum likelihood from incomplete data via the EM algorithm, (with discussion), J. R. Stat. Soc. Ser. B Stat. Methodol. 39 (1997), 1–38.10.1111/j.2517-6161.1977.tb01600.xSuche in Google Scholar
[6] Gupta, R. D.—Kundu, D.: Generalized exponential distributions, Aust. N. Z. J. Stat. 41 (1999), 173–188.10.1111/1467-842X.00072Suche in Google Scholar
[7] Hemmati, F.—Khorram, E.—Rezakhah, S.: A new three-parameter ageing distribution, J. Statist. Plann. Inference 141 (2012), 2266–2275.10.1016/j.jspi.2011.01.007Suche in Google Scholar
[8] Johnson, R. A.—Wiechern, D. W.: Applied Multivariate Statistical Analysis, Prentice Hall, New Jersey, 1992.Suche in Google Scholar
[9] Kundu, D.: Bivariate geometric (maximum) generalized exponential distribution, J. Data Sci. 13 (2015), 693–712.10.6339/JDS.201510_13(4).0004Suche in Google Scholar
[10] Kus, C.: A new lifetime distribution, Comput. Statist. Data Anal. 51 (2007), 4497–4509.10.1016/j.csda.2006.07.017Suche in Google Scholar
[11] Mahmoudi, E.—Jafari, A. A.: Generalized exponential-power series distributions, Comput. Statist. Data Anal. 56 (2012), 4047–4066.10.1016/j.csda.2012.04.009Suche in Google Scholar
[12] Marshall, A. W.—Olkin, I.: A new method of adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), 641–652.10.1093/biomet/84.3.641Suche in Google Scholar
[13] Nekoukhou, V.—Alamatsaz, M. H.—Bidram, H.: Discrete generalized exponential distribution of a second type, Statistics 47(4) (2013), 876–887.10.1080/02331888.2011.633707Suche in Google Scholar
[14] Nekoukhou, V.—Bidram, H.: Exponential-discrete generalized exponential distribution: A new compound model, J. Stat. Theory Appl. 15(2) (2016), 169–180.10.2991/jsta.2016.15.2.7Suche in Google Scholar
[15] Nekoukhou, V.—Alamatsaz, M. H.—Bidram, H.: A note on exponentiated geometric distribution: Another generalization of geometric distribution, Comm. Statist. Theory Methods 45(5) (2016), 1575.10.1080/03610926.2013.864769Suche in Google Scholar
[16] Silva, R. B.—Bourguignon, M.—Dias, C. R. B.—Cordeiro, G. M.: The compound class of extended Weibull power series distributions, Comput. Statist. Data Anal. 58 (2013), 352–367.10.1016/j.csda.2012.09.009Suche in Google Scholar
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Artikel in diesem Heft
- Regular Papers
- Semidistributivity and Whitman Property in implication zroupoids
- Composition of binary quadratic forms over number fields
- On Z-Symmetric Rings
- On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences
- Coefficient estimates for Libera type bi-close-to-convex functions
- Oscillation of nonlinear third-order differential equations with several sublinear neutral terms
- On rapidly oscillating solutions of a nonlinear elliptic equation
- Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type
- Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
- On absolute double summability methods with high indices
- On the continuity of lattice isomorphisms on C(X, I)
- New fixed point theorems for countably condensing maps with an application to functional integral inclusions
- Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations
- The form of locally defined operators in waterman spaces
- Conformal vector fields on almost co-Kähler manifolds
- A certain η-parallelism on real hypersurfaces in a nonflat complex space form
- On log-bimodal alpha-power distributions with application to nickel contents and erosion data
- Univariate and bivariate extensions of the generalized exponential distributions
- Pellian equations of special type
