A new two parameter Burr XII distribution: properties, copula, different estimation methods, and modeling acute bone cancer data
Volume 13, Issue 5, pp 223--238
http://dx.doi.org/10.22436/jnsa.013.05.01
Publication Date: March 03, 2020
Submission Date: December 18, 2019
Revision Date: January 01, 2020
Accteptance Date: January 16, 2020
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Authors
M. M. Mansour
- Department of MIS, Yanbu, Taibah University, Saudi Arabia.
Haitham M. Yousof
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt.
Wahid A. M. Shehata
- Department of Mathematics, Statistics and Insurance, Faculty of Business, Ain Shams University, Egypt.
Mohamed Ibrahim
- Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta, Egypt.
Abstract
We present a new two parameter Burr XII distribution. The new density can be
right skewed with no peak, unimodal-right skewed, left skewed and symmetric.
The new failure rate can be decreasing, unimodal and increasing. Properties
related to the new model are derived. Simple type copula-based construction
is presented for deriving some new bivariate and multivariate type
distributions. The maximum likelihood estimation, Anderson Darling
estimation, right tail Anderson Darling estimation and left tail Anderson
Darling estimation methods are used to estimate the model parameters. A new
data set is analyzed for comparing estimations methods and the competitive
models.
Share and Cite
ISRP Style
M. M. Mansour, Haitham M. Yousof, Wahid A. M. Shehata, Mohamed Ibrahim, A new two parameter Burr XII distribution: properties, copula, different estimation methods, and modeling acute bone cancer data, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 5, 223--238
AMA Style
Mansour M. M., Yousof Haitham M., Shehata Wahid A. M., Ibrahim Mohamed, A new two parameter Burr XII distribution: properties, copula, different estimation methods, and modeling acute bone cancer data. J. Nonlinear Sci. Appl. (2020); 13(5):223--238
Chicago/Turabian Style
Mansour, M. M., Yousof, Haitham M., Shehata, Wahid A. M., Ibrahim, Mohamed. "A new two parameter Burr XII distribution: properties, copula, different estimation methods, and modeling acute bone cancer data." Journal of Nonlinear Sciences and Applications, 13, no. 5 (2020): 223--238
Keywords
- Burr XII distribution
- copula
- asymptotics
- moments
- maximum likelihood method
- Anderson Darling
MSC
References
-
[1]
R. H. M. Abdelkhalek, Extended Poisson-Burr XII Distribution, J. Stat. Appl., 1 (2018), 64--70
-
[2]
M. Aboray, N. S. Butt, Extended Weibull Burr XII Distribution: Properties and Applications, Pak. J. Stat. Oper. Res., 15 (2019), 891--903
-
[3]
A. Z. Afify, G. M. Cordeiro, E. M. M. Ortega, H. M. Yousof, N. S. Butt, The four-parameter Burr XII distribution: properties, regression model, and applications, Comm. Statist. Theory Methods, 47 (2018), 2605--2624
-
[4]
E. Altun, H. M. Yousof, S. Chakraborty, L. Handique, Zografos-Balakrishnan Burr XII distribution: regression modeling and applications, Int. J. Math. Stat., 19 (2018), 46--70
-
[5]
E. Altun, H. M. Yousof, G. G. Hamedani, A new log-location regression model with influence diagnostics and residual analysis, Facta Univ. Ser. Math. Inform., 33 (2018), 417--449
-
[6]
I. W. Burr, Cumulative frequency functions, Ann. Math. Statistics, 13 (1942), 215--232
-
[7]
I. W. Burr, On a general system of distributions, III.The simplerange, J. Amer. Stat. Assoc., 63 (1968), 636--643
-
[8]
I. W. Burr, Parameters for a general system of distributions to match a grid of $\alpha _{\mathit{3}}$ and $\alpha _{\mathit{4}}$, Comm. Statist., 2 (1973), 1--21
-
[9]
I. W. Burr, P. J. Cislak, On a general system of distributions: I. Its curve-shaped characteristics; II. The sample median, J. Amer. Statist. Assoc., 63 (1968), 627--635
-
[10]
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
-
[11]
M. M. Elbiely, H. M. Yousof, A new flexible Weibull Burr XII distribution, J. Stat. Appl., 2 (2019), 59--77
-
[12]
P. Feigl, M. Zelen, Estimation of exponential survival probabilities with concomitant information, Biometrics, 21 (1965), 826--838
-
[13]
I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, Academic Press, San Diego (2000)
-
[14]
M. A. Hatke, A certain cumulative probability function, Ann. Math. Statistics, 20 (1949), 461--463
-
[15]
M. Ibrahim, The compound Poisson Rayleigh Burr XII distribution: properties and applications, J. Appl. Prob. Stat., forthcoming (2019)
-
[16]
A. D. C. Nascimento, K. F. Silva, G. M. Cordeiro, M. Alizadeh, H. M. Yousof, G. G. Hamedani, The odd Nadarajah-Haghighi family of distributions: properties and applications, Studia Sci. Math. Hungar., 56 (2019), 185--210
-
[17]
P. F. Paranaíba, E. M. M. Ortega, G. M. Cordeiro, M. A. R. de Pascoa, The Kumaraswamy Burr XII distribution: theory and practice, J. Stat. Comput. Simul., 83 (2013), 2117--2143
-
[18]
P. F. Paranaíba, E. M. M. Ortega, G. M. Cordeiro, R. R. Pescim, The beta Burr XII distribution with application to lifetime data, Comput. Statist. Data Anal., 55 (2011), 1118--1136
-
[19]
A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series, Vol. 1, Gordon and Breach Science Publishers, Amsterdam (1986)
-
[20]
A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series, Vol. 4, Gordon and Breach Science Publishers, New York (1992)
-
[21]
H. M. Reyad, S. A. Othman, The Top-Leone Burr-XII distribution: Properties and applications, British J. Math. Comput. Sci., 21 (2017), 1--15
-
[22]
R. N. Rodriguez, A Guide to the Burr type XII distributions, Biometrika, 64 (1977), 129--134
-
[23]
P. R. Tadikamalla, A look at the Burr and related distributions, Internat. Statist. Rev., 48 (1980), 337--344
-
[24]
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
-
[25]
H. M. Yousof, E. Altun, T. G. Ramires, M. Alizadeh, M. Rasekhi, A new family of distributions with properties, regression models and applications, J. Stat. Manag. Syst., 21 (2018), 163--188
-
[26]
H. M. Yousof, E. Altun, M. Rasekhi, M. Alizadeh, G. G. Hamedani, M. M. Ali, A new lifetime model with regression models, characterizations and applications, Comm. Statist. Simulation Comput., 48 (2019), 264--286
-
[27]
W. J. Zimmer, J. B. Keats, F. K. Wang, The Burr XII distribution in reliability analysis, J. Quality Tech., 30 (1998), 386--394