Geodesic
The odd inverse Pareto-G class: properties and applications
Aldahlan, Maha A.1 ; Afify, Ahmed Z.2 ; Ahmed, A-Hadi N.3
1 Statistics Department, Faculty of Science, King Abdulaziz University, Jaddeh, KSA;Statistics Department, Faculty of Science, University of Jeddah, Jaddeh, KSA
2 Department of Statistics, Mathematics and Insurance, Benha University, Egypt
3 Department of mathematical statistics, ISSR, Cairo University, Egypt
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 5, p. 278-290.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We introduce a new family of continuous distributions called the \textit{odd inverse Pareto-G} class which extends the exponentiated-G family due to Gupta et al. [R. C. Gupta, P. L. Gupta, R. D. Gupta, Comm. Statist. Theory Methods, $\textbf{27}$ (1998), 887--904] and the Marshall-Olkin-G class due to Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, $\textbf{84}$ (1997), 641--652]. We define and study two special models of the proposed family which are capable of modeling various shapes of aging and failure criteria. The special models of this family can provide reversed J-shape, symmetric, left skewed, right skewed, unimodal or bimodal shapes for the density function. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. By means of four real data sets we show that the special models of this family have superior performance over several existing distributions.
DOI : 10.22436/jnsa.012.05.02
Classification : 62E10, 60E05
Keywords: Generating function, inverse Pareto distribution, maximum likelihood, order statistic, Rényi entropy

Aldahlan, Maha A. 1 ; Afify, Ahmed Z. 2 ; Ahmed, A-Hadi N. 3

1 Statistics Department, Faculty of Science, King Abdulaziz University, Jaddeh, KSA;Statistics Department, Faculty of Science, University of Jeddah, Jaddeh, KSA
2 Department of Statistics, Mathematics and Insurance, Benha University, Egypt
3 Department of mathematical statistics, ISSR, Cairo University, Egypt 
@article{JNSA_2019_12_5_a1,
     author = {Aldahlan, Maha A. and Afify, Ahmed Z. and Ahmed, A-Hadi N.},
     title = {The odd inverse {Pareto-G} class: properties and applications},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {278-290},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {2019},
     doi = {10.22436/jnsa.012.05.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.05.02/}
}
TY  - JOUR
AU  - Aldahlan, Maha A.
AU  - Afify, Ahmed Z.
AU  - Ahmed, A-Hadi N.
TI  - The odd inverse Pareto-G class: properties and applications
JO  - Journal of nonlinear sciences and its applications
PY  - 2019
SP  - 278
EP  - 290
VL  - 12
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.05.02/
DO  - 10.22436/jnsa.012.05.02
LA  - en
ID  - JNSA_2019_12_5_a1
ER  - 
%0 Journal Article
%A Aldahlan, Maha A.
%A Afify, Ahmed Z.
%A Ahmed, A-Hadi N.
%T The odd inverse Pareto-G class: properties and applications
%J Journal of nonlinear sciences and its applications
%D 2019
%P 278-290
%V 12
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.05.02/
%R 10.22436/jnsa.012.05.02
%G en
%F JNSA_2019_12_5_a1
Aldahlan, Maha A.; Afify, Ahmed Z.; Ahmed, A-Hadi N. The odd inverse Pareto-G class: properties and applications. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 5, p. 278-290. doi : 10.22436/jnsa.012.05.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.05.02/

[1] Abdul-Moniem, I. B.; Abdel-Hameed, H. F. On exponentiated Lomax distribution, Int. J. Math. Arch., Volume 3 (2012), pp. 2144-2150

[2] Afify, A. Z.; Altun, E.; Alizadeh, M.; Ozel, G.; G. G. Hamedani The odd exponentiated half-logistic-G family: properties, characterizations and applications, Chil. J. Stat., Volume 8 (2017), pp. 65-91

[3] Afify, A. Z.; Cordeiro, G. M.; Nadarajah, S.; Yousof, H. M.; Ozel, G.; Nofal, Z. M.; Altun, E. The complementary geometric transmuted-G family of distributions: model, properties and application, Hacet. J. Math. Statist., Volume 47 (2018), pp. 1348-1374

[4] Alizadeh, M.; Yousof, H. M.; Afify, A. Z.; Cordeiro, G. M.; Mansoor, M. The Complementary Generalized Transmuted Poisson-G Family of Distributions, Austrian J. Statist., Volume 47 (2018), pp. 51-71 | DOI

[5] Alzaatreh, A.; Lee, C.; Famoye, F. A new method for generating families of distributions, Metron, Volume 71 (2013), pp. 63-79 | DOI

[6] Asgharzadeh, A.; Bakouch, H. S.; Nadarajah, S.; Sharafi, F. A new weighted Lindley distribution with application, Braz. J. Probab. Stat., Volume 30 (2016), pp. 1-27 | Zbl | DOI

[7] Asgharzadeh, A.; Nadarajah, S.; Sharafi, F. Weibull Lindley distribution, REVSTAT, Volume 16 (2018), pp. 87-113 | Zbl

[8] Bourguignon, M.; Silva, R. B.; Cordeiro, G. M. The Weibull-G family of probability distributions, J. Data Sci., Volume 12 (2014), pp. 53-68

[9] Cordeiro, G. M.; Afify, A. Z.; Ortega, E. M. M.; Suzuki, A. K.; Mead, M. E. The odd Lomax generator of distributions: Properties, estimation and applications, J. Comput. Appl. Math., Volume 347 (2019), pp. 222-237 | DOI | Zbl

[10] Cordeiro, G. M.; Afify, A. Z.; Yousof, H. M.; Cakmakyapan, S.; Ozel, G. The Lindley Weibull Distribution: Properties and Applications, Anais da Academia Brasileira de Ciencias, Volume 90 (2018), pp. 2579-2598

[11] Cordeiro, G. M.; Afify, A. Z.; Yousof, H. M.; Pescim, R. R.; Aryal, G. R. The exponentiated Weibull-H family of distributions: Theory and Applications, Mediterr. J. Math., Volume 14 (2017), pp. 1-22 | DOI | Zbl

[12] Cordeiro, G. M.; Castro, M. de A new family of generalized distributions, J. Stat. Comput. Simul., Volume 81 (2011), pp. 883-898 | DOI

[13] Cordeiro, G. M.; Ortega, E. M. M.; Popovic, B. V.; Pescim, R. R. The Lomax generator of distributions: properties, minification process and regression model, Appl. Math. Comput., Volume 247 (2014), pp. 465-486 | Zbl | DOI

[14] Eugene, N.; Lee, C.; Famoye, F. Beta-normal distribution and its applications, Comm. Statist. Theory Methods, Volume 31 (2002), pp. 497-512 | DOI

[15] Ghitany, M. E.; Al-Awadhi, F. A.; Alkhalfan, L. A. Marshall–Olkin extended Lomax distribution and its application to censored data, Comm. Statist. Theory Methods, Volume 36 (2007), pp. 1855-1866 | DOI | Zbl

[16] Ghitany, M. E.; Al-Mutairi, D. K.; Al-Awadhi, F. A.; Al-Burais, M. M. Marshall-Olkin extended Lindley distribution and its application, Int. J. Appl. Math., Volume 25 (2012), pp. 709-721 | Zbl

[17] Gupta, R. C.; Gupta, P. L.; Gupta, R. D. Modeling failure time data by Lehman alternatives, Comm. Statist. Theory Methods, Volume 27 (1998), pp. 887-904 | DOI | Zbl

[18] Kemaloglu, S. A.; Yilmaz, M. Transmuted two-parameter Lindley distribution, Comm. Statist. Theory Methods, Volume 46 (2017), pp. 11866-11879 | DOI | Zbl

[19] Klugman, S. A.; Panjer, H. H.; G. E. Willmot Loss models: from data to decisions, John Wiley & Sons, Hoboken, 2012 | Zbl

[20] Kundu, D.; Raqab, M. Z. Generalized Rayleigh distribution: different methods of estimations, Comput. Statist. Data Anal., Volume 49 (2005), pp. 187-200 | DOI | Zbl

[21] Lee, E. T.; Wang, J. W. Statistical methods for survival data analysis: Third edition, John Wiley & Sons, Hoboken, 2003 | DOI

[22] Lemonte, A. J.; Cordeiro, G. M. An extended Lomax distribution, Statistics, Volume 47 (2013), pp. 800-816 | Zbl | DOI

[23] Lindley, D. V. Fiducial distributions and Bayes’ theorem, J. Roy. Statist. Soc. Ser. B, Volume 20 (1958), pp. 102-107

[24] Marshall, A. W.; Olkin, I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, Volume 84 (1997), pp. 641-652 | DOI

[25] Mudholkar, G. S.; Srivastava, D. K. Exponentiated Weibull family for analyzing bathtub failure-real data, IEEE Trans. Reliab., Volume 42 (1993), pp. 299-302 | DOI

[26] Nadarajah, S.; Bakouch, H. S.; Tahmasbi, R. A generalized Lindley distribution, Sankhya B, Volume 73 (2011), pp. 331-359 | DOI

[27] Proschan, F. Theoretical explanation of observed decreasing failure rate, Technometrics, Volume 5 (1963), pp. 375-383

[28] J. W. S. Rayleigh On the resultant of a large number of vibration of the same pitch and arbitrary phase, Philosophical Magazine: Series 5, Volume 43 (1880), pp. 259-272

[29] Shanker, R.; Mishra, A. A quasi Lindley distribution, African J. Math. Comput. Sci. Res., Volume 6 (2013), pp. 64-71 | DOI

[30] Tahir, M. H.; Cordeiro, G. M.; Mansoor, M.; Zubair, M. The Weibull-Lomax distribution: properties and applications, Hacet. J. Math. Stat., Volume 44 (2015), pp. 455-474 | Zbl | DOI

[31] Torabi, H.; N. H. Montazari The gamma-uniform distribution and its application , Kybernetika (Prague), Volume 48 (2012), pp. 16-30 | EuDML

[32] W. Weibull A statistical distribution function of wide applicability, J. Appl. Mech., Volume 18 (1951), pp. 290-293

[33] Zografos, K.; Balakrishnan, N. On families of beta and generalized gamma generated distributions and associated inference, Stat. Methodol., Volume 6 (2009), pp. 344-362 | Zbl | DOI

Cité par Sources :