JP Journal of Biostatistics

The JP Journal of Biostatistics is a highly regarded open-access international journal indexed in the Emerging Sources Citation Index (ESCI). It focuses on the application of statistical theory and methods in resolving problems in biological, biomedical, and agricultural sciences. The journal encourages the submission of experimental papers that employ relevant algorithms and also welcomes survey articles in the fields of biostatistics and epidemiology.

Submit Article

EXPONENTIATED KAVYA-MANOHARAN BURR X DISTRIBUTION: ESTIMATION UNDER CENSORED TYPE II WITH APPLICATIONS IN MEDICAL DATA

Authors

  • Ibrahim Elbatal
  • Safar M. Alghamdi
  • Anis BEN Ghorbal
  • A. W. Shawki
  • Mohammed Elgarhy
  • Ahmed R. El-Saeed

Keywords:

Kavya-Manoharan Burr X distribution, exponentiated family, moments, maximum likelihood, skewness, kurtosis

DOI:

https://doi.org/10.17654/0973514323013

Abstract

In this article, we introduce a new generalization of Kavya-Manoharan Burr X (KMBx) distribution called exponentiated KMBx (EKMBx) distribution. The EKMBx distribution has three parameters, one scale and two shapes. These parameters make it very flexible. The EKMBx distribution contains three sub-models. Some basic statistical features like; the quantile function, skewness, kurtosis, moments, incomplete moments and generating functions are derived. The maximum likelihood approach is employed to estimate the parameters of the EKMBx model. The flexibility and applicability of the EKMBx model are demonstrated utilizing two different real-world datasets related to medical science.

Received: March 12, 2023 
Accepted: April 24, 2023 

References

W. Barreto-Souza, A. J. Lemonte and G. M. Cordeiro, General results for the Marshall and Olkin’s family of distributions, Anais da Academia Brasileira de Ciências 85 (2013), 3-21.

R. A. Bantan, C. Chesneau, F. Jamal and M. Elgarhy, On the analysis of new COVID-19 cases in Pakistan using an exponentiated version of the M family of distributions, Mathematics 8 (2020), 953. doi:10.3390/math8060953

M. A. Ahmed, M. R. Mahmoud, E. A. ElSherbini, The new Kumaraswamy Kumaraswamy family of generalized distributions with application, Pak. J. Stat. Oper. Res. 11 (2015), 159-180.

Z. M. Nofal, E. Altun, A. Z. Afify and M. Ahsanullah, The generalized Kumaraswamy-G family of distributions, J. Stat. Theory Appl. 18 (2019), 329-342.

A. Mahdavi and D. Kundu, A new method for generating distributions with an application to exponential distribution, Commun. Stat.-Theory Methods 46 (2017), 6543-6557.

P. O. Peter, B. Oluyede, N. Ndwapi and H. Bindele, The Weibull odd Burr III-G family of distributions with properties and applications, Journal of Statistical Modelling: Theory and Applications 2(1) (2021b), 151-180.

R. Silva, F. Gomes-Silva, M. Ramos, G. Cordeiro, P. Marinho and T. A. De Andrade, The exponentiated Kumaraswamy-G class: general properties and application, Rev. Colomb. De Estadística 42 (2019), 1-33.

A. Algarni, A. M. Almarashi, I. Elbatal, A. S. Hassan, E. M. Almetwally, A. M. Daghistani and M. Elgarhy, Type I half logistic Burr XG family: Properties, Bayesian, and non-Bayesian estimation under censored samples and applications to COVID-19 data, Math. Probl. Eng. 2021. https://doi.org/0.1155/2021/5461130

A. A. Al-Babtain, I. Elbatal, H. Al-Mofleh, A. M. Gemeay, A. Z. Afify and A. M. Sarg, The flexible Burr X-G family: properties, inference, and applications in engineering science, Symmetry 13(3) (2021), 474.

G. Cordeiro, E. Ortega and D. C. da Cunha, The exponentiated generalized class of distributions, J. Data Sci. 11 (2013), 1-27.

R. M. I. Arshad, M. H. Tahir, C. Chesneau, F. Jamal, M. Mansoor, M. Zubair and M. Nasir, The gamma Kumaraswamy-G family of distributions: theory, inference and applications, Statistics in Transition New Series 21(5) (2020), 17-40.

A. Zubair, M. Elgarhy, G. Hamedani and N. Butt, Odd generalized N-H generated family of distributions with application to exponential model, Pak. J. Stat. Oper. Res. 16 (2020), 53-71.

B. Lahcene, A new extended-gamma family of distributions: properties and applications, Journal of Applied Mathematics and Computation 5(1) (2021), 9-17.

E. S. El-Sherpieny and M. Elsehetry, Kumaraswamy type I half logistic family of distributions with applications, Gazi Univ. J. Sci. 32 (2019), 333-349.

M. M. Ristic and N. Balakrishnan, The gamma exponentiated exponential distribution, Journal of Statistical Computation and Simulation 82(8) (2012), 1191-1206.

S. Chakraborty, L. Handique and F. Jamal, The Kumaraswamy Poisson-G family of distribution: Its properties and applications, Ann. Data Sci. 9 (2020), 229-247.

L. Handique and S. Chakraborty, The Beta generalized Marshall-Olkin Kumaraswamy-G family of distributions with applications, Int. J. Agricult. Stat. Sci. 13 (2017), 721-733.

H. M. Yousof, A. Z. Afify, G. Hamedani and G. R. Aryal, The Burr X generator of distributions for lifetime data, Journal of Statistical Theory and Applications 16(3) (2017), 288-305.

M. Bourguignon, R. B. Silva and G. M. Cordeiro, The Weibull-G family of probability distributions, J. Data Sci. 12 (2014), 1253-1268.

A. S. Hassan, M. Elgarhy and M. Shakil, Type II half logistic family of distributions with applications, Pak. J. Stat. Oper. Res. 13 (2017), 245-264.

L. Souza, W. R. de Oliveira, C. C. R. de Brito, C. Chesneau, R. Fernandes and T. A. E. Ferreira, Sec-G class of distributions: properties and applications, Symmetry 14 (2022), 299. https://doi.org/0.3390/sym14020299

N. Alotaibi, I. Elbatal, E. M. Almetwally, S. A. Alyami, A. S. Al-Moisheer and M. Elgarhy, Truncated Cauchy power Weibull-G class of distributions: Bayesian and Non-Bayesian inference modelling for COVID-19 and carbon fiber data, Mathematics 10 (2022), 1565.

I. Elbatal, N. Alotaibi, E. M. Almetwally, S. A. Alyami and M. Elgarhy, On Odd PerU3-G class of distributions: properties, regression model, discretization, Bayesian and Non-Bayesian estimation, and applications, Symmetry 14 (2022), 883.

A. A. Al-Babtain, I. Elbatal, C. Chesneau and M. Elgarhy, Sine Topp-Leone-G family of distributions: theory and applications, Open Phys. 18 (2020), 574-593.

S. Chakraborty and L. Handique, Properties and data modelling applications of the Kumaraswamy generalized Marshall-Olkin-G family of distributions, J. Data Sci. 605 (2017), 620.

R. A. Bantan, F. Jamal, C. Chesneau and M. Elgarhy, A new power Topp-Leone generated family of distributions with applications, Entropy 21 (2019), 1177.

https://doi.org/0.3390/e21121177

R. A. Bantan, F. Jamal, C. Chesneau and M. Elgarhy, Truncated inverted Kumaraswamy generated family of distributions with applications, Entropy 21 (2019), 1089. https://doi.org/10.3390/e21111089

M. M. Badr, I. Elbatal, F. Jamal, C. Chesneau and M. Elgarhy, The transmuted odd Fréchet-G family of distributions: Theory and applications, Mathematics 8 (2020), 958.

M. Alizadeh, M. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair and G. Hamedani, The Kumaraswamy Marshal-Olkin family of distributions, J. Egypt. Math. Soc. 23 (2015), 546-557.

P. Kavya and M. Manoharan, Some parsimonious models for lifetimes and applications, J. Statist. Comput. Simul. 91 (2021), 3693-3708.

I. W. Burr, Cumulative frequency functions, Ann. Math. Stat. 13(2) (1942), 215-232.

J. G. Surles and W. J. Padgett, Inference for reliability and stress-strength for a scaled Burr Type X distribution, Lifetime Data Anal. 7(2) (2001), 187-200.

O. H. M. Hassan, I. Elbatal, A. H. Al-Nefaie and M. Elgarhy, On the Kavya-Manoharan-Burr X model: estimations under ranked set sampling and applications, Journal of Risk and Financial Management 16 (2023), 19.

https://doi.org/10.3390/jrfm16010019A

J. P. Klein and M. L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, Springer: Berlin/Heidelberg, Germany, 2006.

T. Bjerkedal, Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Epidemiol. 72(1) (1960), 130-148.

S. M. Behairy, G. R. Al-Dayian and A. A. El-Helbawy, The Kumaraswamy-Burr type III-distribution: properties and estimation, J. Adv. Math. Comput. Sci. 14(2) (2016), 1-21.

G. R. AL-Dayian, Burr type III distribution: properties and estimation, The Egyptian Statistical Journal 43 (1999), 102-116.

Published

2023-06-08

Issue

Section

Articles

How to Cite

EXPONENTIATED KAVYA-MANOHARAN BURR X DISTRIBUTION: ESTIMATION UNDER CENSORED TYPE II WITH APPLICATIONS IN MEDICAL DATA. (2023). JP Journal of Biostatistics, 23(3), 227-247. https://doi.org/10.17654/0973514323013

Similar Articles

1-10 of 27

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)