The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test
Volume 12, Issue 5, pp 314--336
http://dx.doi.org/10.22436/jnsa.012.05.05
Publication Date: January 05, 2019
Submission Date: September 14, 2019
Revision Date: October 05, 2019
Accteptance Date: November 17, 2019
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Authors
T. H. M. Abouelmagd
- Management Information System Department, Taibah University, Saudi Arabia.
Mohammed S. Hamed
- Management Information System Department, Taibah University, Saudi Arabia.
G. G. Hamedani
- Department of Mathematics, Statistics and Computer Science, Marquette University, USA.
M. Masoom Ali
- Department of Mathematical Sciences, Ball State University, Muncie, USA.
Hafida Goual
- Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria.
Mustafa C. Korkmaz
- Department of Measurement and Evaluation, Artvin Coruh University, Artvin, TURKEY.
Haitham M. Yousof
- Department of Statistics, Mathematics and Insurance, Benha University, Egypt.
Abstract
The goal of this work is to introduce a new family of continuous
distributions with a strong physical applications. Some statistical
properties are derived, and certain useful characterizations of the proposed
family of distributions are presented. Five applications are provided to
illustrate the importance of the new family. A modified goodness-of- fit
test for the new family in complete data case are investigated via two
examples. We propose, as a first step, the construction of
Nikulin-Rao-Robson statistic based on chi-squared fit tests for the new
family in the case of complete data. The new test is based on the
Nikulin-Rao-Robson statistic separately proposed by [M. S. Nikulin, Theory
Probab. Appl., \(\textbf{18}\) (1974), 559--568] and [K. C. Rao, B. S.
Robson, Comm. Statist., \(\textbf{3}\) (1974), 1139--1153]. As a second step,
an application to real data has been proposed to show the applicability of
the proposed test.
Share and Cite
ISRP Style
T. H. M. Abouelmagd, Mohammed S. Hamed, G. G. Hamedani, M. Masoom Ali, Hafida Goual, Mustafa C. Korkmaz, Haitham M. Yousof, The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 5, 314--336
AMA Style
Abouelmagd T. H. M., Hamed Mohammed S., Hamedani G. G., Ali M. Masoom, Goual Hafida, Korkmaz Mustafa C., Yousof Haitham M., The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test. J. Nonlinear Sci. Appl. (2019); 12(5):314--336
Chicago/Turabian Style
Abouelmagd, T. H. M., Hamed, Mohammed S., Hamedani, G. G., Ali, M. Masoom, Goual, Hafida, Korkmaz, Mustafa C., Yousof, Haitham M.. "The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test." Journal of Nonlinear Sciences and Applications, 12, no. 5 (2019): 314--336
Keywords
- Validation test
- maximum likelihood estimation
- generating function
- moments
- zero truncated Poisson
MSC
References
-
[1]
T. H. M. Abouelmagd, A new flexible version of the Lomax distribution with applications, Int. J. Stat. Probab., 7 (2018), 120–132.
-
[2]
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.
-
[3]
A. Z. Afify, Z. M. Nofal, A. N. Ebraheim, Exponentiated transmuted generalized Rayleigh distribution: A new four parameter Rayleigh distribution, Pak. J. Stat. Oper. Res., 11 (2015), 115–134.
-
[4]
A. Z. Afify, H. M. Yousof, G. M. Cordeiro, E. M. M. Ortega, Z. M. Nofal, The Weibull Fréchet distribution and its applications, J. Appl. Statist., 43 (2016), 2608–2626.
-
[5]
G. R. Aryal, H. M. Yousof , The exponentiated generalized-G Poisson family of distributions, Stoch. Qual. Control, 32 (2017), 7–23.
-
[6]
V. Bagdonavicius, J. Kruopis, M. S. Nikulin, Non-parametric tests for complete data, John Wiley & Sons, Hoboken (2011)
-
[7]
V. Bagdonavicius, R. Levuliené, M. S. Nikulin, Q. X. Tran, On chi-squared type tests and their applications in survival analysis and reliability, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 408 (2012), 43–61.
-
[8]
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.
-
[9]
G. M. Cordeiro, A. Z. Afify, H. M. Yousof, R. R. Pescim, G. R. Aryal, The exponentiated Weibull-H family of distributions: Theory & Applications, Mediterr. J. Math., 14 (2017), 22 pages.
-
[10]
G. M. Cordeiro, E. M. Hashimoto, E. M. M. Ortega, The McDonald Weibull model, Statistics, 48 (2014), 256–278.
-
[11]
G. M. Cordeiro, E. M. M. Ortega, S. Nadarajah, The Kumaraswamy Weibull distribution with application to failure data, J. Franklin Inst., 347 (2010), 1399–1429.
-
[12]
G. M. Cordeiro, E. M. M. Ortega, B. V. Popovic, The Gamma-Lomax distribution, J. Stat. Comput. Simul., 85 (2015), 305–319.
-
[13]
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.
-
[14]
F. Drost , Asymptotics for generalized chi-squared goodness-of-fit tests, CWI Tracs, Centre for Mathematics and Computer Sciences, Amsterdam (1988)
-
[15]
W. Glänzel , A characterization theorem based on truncated moments and its application to some distribution families, in: Mathematical Statistics and Probability Theory, 1986 (1986), 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 Lehman alternatives, Comm. Statist. Theory Methods, 27 (1998), 887–904.
-
[18]
G. G. Hamedani, H. M. Yousof, M. Rasekhi, M. Alizadeh, S. M. Najibi , Type I general exponential class of distributions, Pak. J. Stat. Oper. Res., 14 (2018), 39–55.
-
[19]
G. G. Hamedani, M. Rasekhi, S. M. Najibi, H. M. Yousof, M. Alizadeh, Type II general exponential class of distributions, Pak. J. Stat. Oper. Res., forthcoming (2018)
-
[20]
C. S. Kakade, D. T. Shirke, Tolerance interval for exponentiated exponential distribution based on grouped data, Int. J. Agric. Stat. Sci., 3 (2007), 625–631.
-
[21]
M. N. Khan, The modified beta Weibull distribution, Hacet. J. Math. Stat., 44 (2015), 1553–1568.
-
[22]
M. S. Khan, R. King, Transmuted modified Weibull distribution: a generalization of the modified Weibull probability distribution, Eur. J. Pure Appl. Math., 6 (2013), 66–88.
-
[23]
M. Ç. Korkmaz, A. I. Genç, Two-Sided Generalized Exponential Distribution, Comm. Statist. Theory Methods, 44 (2015), 5049–5070.
-
[24]
C. Lee, F. Famoye, O. Olumolade, Beta-Weibull distribution: some properties and applications to censored data, J. Modern Appl. Statist. Methods, 6 (2007), 173–186.
-
[25]
A. J. Lemonte, G. M. Cordeiro, An extended Lomax distribution, Statistics, 47 (2013), 800–816.
-
[26]
K. S. Lomax, Business failures: Another example of the analysis of failure data, J. Amer. Statist. Assoc., 49 (1954), 847–852.
-
[27]
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.
-
[28]
D. N. P. Murthy, M. Xie, R. Jiang, Weibull Models, Wiley-Interscience, [John Wiley & Sons], Hoboken (2004)
-
[29]
M. S. Nikulin, Chi-square test for continuous distribution with shift and scale parameters, Theory Probab. Appl., 18 (1974), 559–568.
-
[30]
S. B. Provost, A. Saboor, M. Ahmad , The Gamma–Weibull distribution, Pakistan J. Statist., 27 (2011), 111–131.
-
[31]
K. C. Rao, B. S. Robson, A chi-squabe statistic for goodies-of-fit tests within the exponential family, Comm. Statist., 3 (1974), 1139–1153.
-
[32]
S. Rezaei, S. Nadarajah, N. Tahghighnia, New three-parameter lifetime distribution, Statistics, 47 (2013), 835–860.
-
[33]
M. M. Ristic, N. Balakrishnan, The Gamma-exponentiated exponential distribution, J. Stat. Comput. Simul., 82 (2012), 1191–1206.
-
[34]
M. H. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, The Weibull-Lomax distribution: properties and applications, Hacet. J. Math. Stat., 44 (2015), 455–474.
-
[35]
A. W. van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge (1998)
-
[36]
V. Voinov, R. Alloyarova, N. Pya, Recent achievements in modified chi-squared goodness-of-fit testing, in: Statistical Models and Methods for Biomedical and Technical Systems, 2008 (2008), 241–258.
-
[37]
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.
-
[38]
H. M. Yousof, A. Z. Afify, G. G. Hamedani, G. Aryal, The Burr X generator of distributions for lifetime data, J. Stat. Theory Appl., 16 (2017), 288–305.
-
[39]
H. M. Yousof, M. Alizadeh, S. M. A. Jahanshahiand, T. G. Ramires, I. Ghosh, G. G. Hamedani, The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, J. Data Sci., 15 (2017), 723–740.
-
[40]
H. M. Yousof, E. Altun, T. G. Ramires, M. Alizadeh, M. Rasekhi , A new family of distributions with properties, regression models and applications, J. Statist. Manag. Syst., 21 (2018), 163–188.
-
[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, Pakistan J. Statist., 33 (2017), 95–116.