The Type II Topp-Leone-G Power Series Distribution with Applications on Bladder Cancer

Boikanyo Makubate; Marang  Matsuokwane; Broderick O. Oluyede; Lesego Gabaitiri; Simbarashe Chamunorwa

doi:10.46481/jnsps.2022.848

Authors

Boikanyo Makubate
makubateb@biust.ac.bw
Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana https://orcid.org/0000-0002-1581-3165
Marang Pearl Matsuokwane Botswana International University of Science & Technology
Broderick O. Oluyede otswana International University of Science and Technology, P. Bag 16, Palapye, Botswana
Lesego Gabaitiri Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana
Simbarashe Chamunorwa Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana

Keywords:

Type II Topp-Leone-G Distribution, Power Series Distribution, Maximum Likelihood Estimation

Abstract

Statistical distributions are important in modeling the real life of an item and therefore proper distributions that provide useful information for sound conclusions and decisions are needed. For that reason, the demand for developing new generalized distributions have become appropriate for data that have both monotonic and non-monotonic hazard rate functions. In this paper, we develop a new distribution called the Type II Topp-Leone-G Power Series (TIITLGPS) distribution by compounding the Type II Topp-Leone-G (TIITLG) distribution with the power series distribution. Statistical properties of the TIITLGPS distribution are obtained. A variety of shapes for the densities and hazard rate are presented of the considered special case. A simulation study to examine the efficiency of the maximum likelihood estimates is also conducted. Finally, the bladder cancer data example is analyzed for illustrative purposes, it is displayed that the introduced distribution provides better fit when compared to other non-nested distributions considered in this work.

Dimensions

REFERENCES

C. W. Topp & F. C. Leone, ”A Family of J-shaped Frequency Functions”, Journal of the American Statistical Association 50 (1955) 209. DOI: http://dx.doi.org/10.1080/01621459.1955.10501259. DOI: https://doi.org/10.1080/01621459.1955.10501259

M. E. Ghitany, S. Kotz & M. Xie, ”On Some Reliability Measures and their Stochastic Orderings for the Topp-Leone Distribution”, Journal of Applied Statistics 32 (2005) 715. DOI: https://doi.org/10.1080/02664760500079613 DOI: https://doi.org/10.1080/02664760500079613

D. Vicaria, J. R. V. Dorp & S. Kotz, ”Two-Sided Generalized Topp and Leone (TS-GTL) Distributions”, Journal of Applied Statistics 35 (2008) 1115. DOI: https://doi.org/10.1080/02664760802230583

B. Oluyede, S. Chamunorwa, F. Chipepa & M. Alizadeh, ”The Topp-Leone-Gompertz-G Family of Distributions with Applications”, Journal of Statistics and Management Systems (2022) DOI https://doi.org/10.1080/09720510.2021.1972623. DOI: https://doi.org/10.1080/09720510.2021.1972623

S. Chamunorwa, B. Oluyede, B. Makubate & F. Chipepa ”The exponentiated OddWeibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications”, Pakistan Journal of Statistics 37 (2021) 143-158. Doi: https://www.pakjs.com/wp-content/uploads/2021/03/372-05.pdf.

A. Hassan, M. Elgarhy, & A. Zubair, ”Type II Generalized Topp-Leone Family of Distributions: Properties and Applications”, Journal of data science: JDS (2019) doi: 10.6339/JDS.201910 17(4).0001. DOI: https://doi.org/10.6339/JDS.201910_17(4).0001

A. Al-Shomrani, O.Arif, A. Shawky, S. Hanif & M. Q. Shahbaz, ”Topp Leone Family of Distributions: Some Properties and Application”, Pakistan Journal of Statistics and Operation Research 12 (2016) 443. DOI: 10.18187/pjsor.v12i3.1458. DOI: https://doi.org/10.18187/pjsor.v12i3.1458

M. Elgarhy, M. Arslan Nasir, F.Jamal & G. Gamze Ozel, ”The Type II Topp-Leone Generated Family of Distributions : Properties and Applications”, Journal of Statistics and Management Systems 21 (2018) 1529- DOI: https://doi.org/10.1080/09720510.2018.1516725

DOI: https://doi.org/10.1080/09720510.2018.1516725. [9] N. L. Johnson, S. Kotz & N. Balakrishnan, Continuous Distributions, Volume 1, John Wiley and Sons, New York, NY (1994).

B. Makubate, B. Oluyede & M. Gabanakgosi, ”A New Lindley-Burr XII Distribution: Model, Properties and Applications”, International Journal of Statistics and Probability 10 (2021) 33. DOI:10.5539/ijsp.v10n4p33 DOI: https://doi.org/10.5539/ijsp.v10n4p33

B. Makubate, B. Oluyede & G. Motsewabagale, ”Dagum Power Series Class of Distribution with Applications to Lifetime Data”, Research and Reviews: Journal of Statistics and Mathematical Sciences, 92 (2019) 76.

R. V. da Silva, F. Gomes-Silva, M.W. A. Ramos, G. M. Cordeiro & E. M. M. Ortega, ”The Exponentiated Burr XII Poisson Distribution with Application to Lifetime Data”, International Journal of Statistics and Probability

(2015) 1399.

R. C. Gupta, P. L. Gupta & R. D. Gupta, ”Modeling failure time data by Lehmann alternatives”,Comm. Statist. Theory Methods 27 (1998) 887. DOI: https://doi.org/10.1080/03610929808832134

R. D.Gupta & D. Kundu, ”Generalized exponential distributions”, Aust.N.Z.J.Stat. 41 (1999) 173-188. DOI: https://doi.org/10.1111/1467-842X.00072

M. C. Korkmaz, H. M. Yousof & Hamedani, G. G., ”The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications”, Journal of Statistical Theory and Applications 17 (2018)

-571.DOI: https://doi.org/10.2991/jsta.2018.17.3.10 DOI: https://doi.org/10.2991/jsta.2018.17.3.10

G. S. Mudholkar & D. K. Srivastava, ”Exponentiated Weibull family for analysing bathtub failure rate data”, IEEE Trans. Reliab. 42 (1993) 299. DOI: https://doi.org/10.1109/24.229504

G. S. Mudholkar, D. K. Srivastava & Freimer, M., ”The Exponentiated Weibull family: A reanalysis of the bus-motor-failure data”, Technometrics 37 (1995) 436. DOI: https://doi.org/10.2307/1269735 DOI: https://doi.org/10.1080/00401706.1995.10484376

S. Nadarajah, ”The Exponentiated Gumbel distribution with climate application”, Environmetrics 17 (2005) 13-23. DOI: https://doi.org/10.1002/env.739 DOI: https://doi.org/10.1002/env.739

S. Nadarajah & Kotz, S., ”The Exponentiated-type distributions”, Acta Appl. Math. 92 (2006) 97-111. DOI: https://doi.org/10.1007/s10440-006-9055-0 DOI: https://doi.org/10.1007/s10440-006-9055-0

S. Nadarajah & A. K.Gupta, ”The Exponentiated gamma distribution with application to drought data”, Calcutta Statist. Assoc. Bull. 59 (2007) 29. DOI: https://doi.org/10.1177/0008068320070103

M. Pararai, G. Warahena-Liyanage & B.Oluyede, ”Exponentiated Power Lindley Poisson Distribution: Properties and Application”, Communications in Statistics-Theory and Methods 46 (2017) 4726-4755, doi: 10.1080/03610926.2015.1076473. DOI: https://doi.org/10.1080/03610926.2015.1076473

J. Chambers, W. Cleveland, B. Kleiner & P. Tukey, ”Graphical Methods of Data Analysis”, Chapman and Hall (1983)

G. Chen&N. Balakrishnan, ”A General Purpose Approximate Goodnessof- Fit Test”, Journal of Quality Technology 27 (1995) 154. DOI:

https://doi.org/10.1080/00224065.1995.11979578 DOI: https://doi.org/10.1080/00224065.1995.11979578

B. Oluyede, B. Mashabe, A. Fagbamigbe, B. Makubate & D. Wanduku,”The Exponentiated Generalized Power Series: Family of Distributions: Theory, Properties and Applications”, Heliyon 6 (2020) doi: 10.1016/j.heliyon.2020.e04653. DOI: https://doi.org/10.1016/j.heliyon.2020.e04653

B. Oluyede, F. Chipepa & D. Wanduku, ”The Odd Weibull-Topp-Leone-G Power Series Family of Distributions: Model, Properties, and Applications”, Journal of Nonlinear Science and Application 14 (2021) 60 doi: 10.22436/jnsa.014.04.06. DOI: https://doi.org/10.22436/jnsa.014.04.06

F. Chipepa, B. Oluyede & B. Makubate, ”A New Generalized Family of Odd Lindley-G Distributions with Application”, International Journal of Statistics and Probability 8 (2019) doi:10.5539/ijsp.v8n6p1. DOI: https://doi.org/10.5539/ijsp.v8n6p1

E. T.Lee & J. W. Wang, Statistical Methods for Survival Data Analysis, 3rd Edn., JohnWiley and Sons, New York, ISBN: 9780471458555 (2003) 534. DOI: https://doi.org/10.1002/0471458546