The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations
-
1712
Downloads
-
3174
Views
Authors
Haitham M. Yousof
- Department of Statistics, Mathematics and Insurance, Benha University, Egypt.
Mahdi Rasekhi
- Department of Statistics, Malayer University, Malayer, Iran.
Morad Alizadeh
- Department of Statistics, Faculty of Sciences, Persian Gulf University, Bushehr, 75169, Iran.
G. G. Hamedani
- Department of Mathematics, Statistics and Computer Science, Marquette University, USA.
Abstract
In this paper, we propose and study a new class of continuous distributions
called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which
extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, \(\bf 84\) (1997), 641--652].
Some of its mathematical properties including explicit expressions for the
ordinary and incomplete moments, generating function, order statistics and
probability weighted moments are derived. Some characterizations for the new
family are presented. Maximum likelihood estimation for the model parameters
under uncensored and censored data is addressed in Section 5 as well as a
simulation study to assess the performance of the estimators. The importance
and flexibility of the new family are illustrated by means of two
applications to real data sets.
Share and Cite
ISRP Style
Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, G. G. Hamedani, The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 1, 34--52
AMA Style
Yousof Haitham M., Rasekhi Mahdi, Alizadeh Morad, Hamedani G. G., The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations. J. Nonlinear Sci. Appl. (2020); 13(1):34--52
Chicago/Turabian Style
Yousof, Haitham M., Rasekhi, Mahdi, Alizadeh, Morad, Hamedani, G. G.. "The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations." Journal of Nonlinear Sciences and Applications, 13, no. 1 (2020): 34--52
Keywords
- Marshall-Olkin family
- characterizations
- censored Data
- generating function
- order statistics
- maximum likelihood estimation
MSC
References
-
[1]
M. V. Aarset, How to Identify Bathtub Hazard Rate, IEEE Trans. Reliab., 36 (1987), 106--108
-
[2]
A. Z. Afify, M. Alizadeh, H. M. Yousof, G. Aryal, M. Ahmad, The transmuted geometric-G family of distributions: theory and applications, Pakistan J. Statist., 32 (2016), 139--160
-
[3]
A. Z. Afify, G. M. Cordeiro, H. M. Yousof, A. Alzaatreh, Z. M. Nofal, The Kumaraswamy transmuted-G family of distributions: properties and applications, J. Data Sci., 14 (2016), 245--270
-
[4]
A. Z. Afify, H. M. Yousof, S. Nadarajah, The beta transmuted-H family for lifetime data, Stat. Inference, 10 (2017), 505--520
-
[5]
M. Alizadeh, G. M. Cordeiro, E. de Brito, C. G. B. Demetrio, The beta Marshall-Olkin family of distributions, J. Stat. Distrib. Appl., 2 (2015), 18 pages
-
[6]
M. Alizadeh, M. H. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, G. G. Hamedani, The Kumaraswamy Marshal-Olkin family of distributions, J. Egyptian Math. Soc., 23 (2015), 546--557
-
[7]
M. Alizadeh, H. M. Yousof, A. Z. Afify, G. M. Cordeiro, M. Mansoor, The complementary generalized transmuted poisson-G family, Austrian J. Stat., 47 (2018), 60--80
-
[8]
A. Alzaatreh, C. Lee, F. Famoye, A new method for generating families of continuous distributions, Metron, 71 (2013), 63--79
-
[9]
A. Alzaghal, F. Famoye, C. Lee, Exponentiated T-X family of distributions with some applications, Int. J. Probab. Stat., 2 (2013), 31--49
-
[10]
A. Azzalini, A class of distributions which include the normal, Scand. J. Statist., 12 (1985), 171--178
-
[11]
E. Brito, G. M. Cordeiro, H. M. Yousof, M. Alizadeh, G. O. Silva, Topp-Leone Odd Log-Logistic Family of Distributions, J. Stat. Comput. Simul., 87 (2017), 3040--3058
-
[12]
G. M. Cordeiro, E. M. M. Ortega, D. C. C. da Cunha, The exponentiated generalized class of distributions, J. Data Sci., 11 (2013), 1--27
-
[13]
G. M. Cordeiro, E. M. M. Ortega, B. V. Popović, The gamma-Lomax distribution, J. Stat. Comput. Simul., 85 (2013), 305--319
-
[14]
G. M. Cordeiro, H. M. Yousof, T. G. Ramires, E. M. M. Ortega, The Burr XII system of densities: properties, regression model and applications, J. Stat. Comput. Simul., 88 (2018), 432--456
-
[15]
W. Glänzel, A characterization theorem based on truncated moments and its application to some distribution families, Mathematical statistics and probability theory, Vol. B (Bad Tatzmannsdorf, 1986), 1987 (1987), 75--84
-
[16]
W. Glänzel, Some consequences of a characterization theorem based on truncated moments, Statistics, 21 (1990), 613--618
-
[17]
R. C. Gupta, P. L. Gupta, R. D. Gupta, Modeling failure time data by Lehmann alternatives, Comm. Statist. Theory Methods, 27 (1998), 887--904
-
[18]
R. D. Gupta, D. Kundu, Generalized exponential distributions, Aust. N. Z. J. Stat., 41 (1999), 173--188
-
[19]
. G. Hamedani, E. Altun, M. C. Korkmaz, H. M. Yousof, N. S. Butt, A new extended G family of continuous distributions with mathematical properties, characterizations and regression modeling, Pak. J. Stat. Oper. Res., 14 (2018), 737--758
-
[20]
M. C. Korkmaz, E. Altun, H. M. Yousof, G. G. Hamedani, The odd power Lindley generator of probability distributions: properties, characterizations and regression modeling, Int. J. Stat. Probab., 8 (2019), 70--89
-
[21]
M. R. Leadbetter, G. Lindgren, H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York-Berlin (1983)
-
[22]
C. Lee, F. Famoye, O. Olumolade, Beta-Weibull distribution: some properties and applications to censored data, J. Modern Appl. Stat. Methods, 6 (2007), 173--186
-
[23]
E. T. Lee, J. W. Wang, Statistical Methods for Survival Data Analysis, Wiley-Interscience [John Wiley & Sons], Hoboken (2003)
-
[24]
A. J. Lemonte, G. M. Cordeiro, An extended Lomax distribution, Statistics, 47 (2013), 800--816
-
[25]
A. W. Marshall, I. Olkin, A new methods for adding a parameter to a family of distributions with application to the Exponential and Weibull families, Biometrika, 84 (1997), 641--652
-
[26]
F. Merovci, M. Alizadeh, H. M. Yousof, G. G. Hamedani, The exponentiated transmuted-G family of distributions: theory and applications, Comm. Statist. Theory Methods, 46 (2017), 10800--10822
-
[27]
G. S. Mudholkar, D. K. Srivastava, Exponentiated Weibull family for analysing bathtub failure rate data, IEEE Trans. Reliab., 42 (1993), 299--302
-
[28]
S. Nadarajah, The exponentiated Gumbel distribution with climate application, Environmetrics, 17 (2006), 13--23
-
[29]
S. Nadarajah, G. M. Cordeiro, E. M. M. Ortega, The Zografos Balakrishnan-G family of distributions: Mathematical properties and applications, Comm. Statist. Theory Methods, 44 (2015), 186--215
-
[30]
S. Nadarajah, A. K. Gupta, The exponentiated gamma distribution with application to drought data, Calcutta Statist. Assoc. Bull., 59 (2007), 29--54
-
[31]
Z. M. Nofal, A. Z. Afify, H. M. Yousof, G. M. Cordeiro, The generalized transmuted-G family of distributions, Comm. Statist. Theory Methods, 46 (2017), 4119--4136
-
[32]
M. M. Ristić, D. Kundu, Generalized exponential geometric extreme distribution, J. Stat. Theory Pract., 10 (2016), 179--201
-
[33]
H. V. Roberts, Data Analysis for Managers with Minitab, Scientific Press, Redwood City (1988)
-
[34]
S. M. Salman, P. Sangadji, Total time on test plot analysis for mechanical component of the reactor, Atom Indones, 25 (1999), 61--155
-
[35]
W. T. Shaw, I. R. C. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv, 2007 (2007), 28 pages
-
[36]
D. T. Shirke, C. S. Kakade, On exponentiated lognormal distribution, Int. J. Agricultural Stat. Sci., 2 (2006), 319--326
-
[37]
G. O. Silva, E. M. M. Ortega, G. M. Cordeiro, The beta modified Weibull distribution, Lifetime Data Anal., 16 (2010), 409--430
-
[38]
S. Stollmack, C. M. Harris, Failure-rate analysis applied to recidivism data, Oper. Res., 22 (1974), 1192--1205
-
[39]
H. M. Yousof, A. Z. Afify, M. Alizadeh, N. S. Butt, G. G. Hamedani, M. M. Ali, The transmuted exponentiated generalized-G family of distributions, Pak. J. Stat. Oper. Res., 11 (2015), 441--464
-
[40]
H. M. Yousof, A. Z. Afify, G. G. Hamedani, G. Aryal, The Burr X generator of distributions for lifetime data, Journal of Statistical Theory and Applications, 16 (2017), 288--305
-
[41]
H. M. Yousof, M. Rasekhi, A. Z. Afify, I. Ghosh, M. Alizadeh, G. G. Hamedani, The beta Weibull-G family of distributions:theory, characterizations and applications, Pak. J. Statist., 33 (2017), 95--116
-
[42]
K. Zografos, N. Balakrishnan, On families of beta and generalized gamma-generated distributions and associated inference, Stat. Methodol., 6 (2009), 344--362