Alpha Power-Kumaraswamy Distribution with An Application on Survival Times of Cancer Patients

Authors

  • Fatima Ulubekova

    Department of Statistics, Hacettepe University Ankara, Turkey
  • Gamze Ozel Department of Statistics, Hacettepe University Ankara, Turkey

DOI:

https://doi.org/10.30564/jcsr.v2i2.1855

Abstract

The aim of the study is to obtain the alpha power Kumaraswamy (APK) distribution. Some main statistical properties of the APK distribution are investigated including survival, hazard rate and quantile functions, skewness, kurtosis, order statistics. The hazard rate function of the proposed distribution could be useful to model data sets with bathtub hazard rates. We provide a real data application and show that the APK distribution is better than the other compared distributions fort the right-skewed data sets.

Keywords:

Alpha power transformation; Maximum likelihood estimation

References

[1] Kumaraswamy, P.. Sine Power Probability Density Function. J. Hydrol., 1976, 31(1-2): 181–184. https://doi.org/10.1016/0022-1694(76)90029-9

[2] Kumaraswamy, P.. Extended Sine Power Probability Density Function. J. Hydrol., 1978, 37(1-2): 81–89. https://doi.org/10.1016/0022-1694(78)90097-5

[3] Kumaraswamy,P.. AGeneralizedProbabilityDensityFunctionforDoubleBounded Random Processes. J. Hydrol., 1980, 46(1-2): 79–88, https://doi.org/10.1016/0022-1694(80)90036-0

[4] Sundar, V., Subbiah, K.. Application of Double Bounded Probability Density Function for Analysis of Ocean Waves. Ocean Eng., 1989, 16(2): 193–200, https://doi.org/10.1016/0029-8018(89)90005-X

[5] Fletcher, S. C., Ponnamblam, K.. Estimation of Reservoir Yield and Storage Distribution Using Moments Analysis. J. Hydrol., Vol. 182, Nos. 1–4, 1996, 182(1-4): 259–275, https://doi.org/10.1016/0022-1694(95)02946-X

[6] Mitnik, P.. New Properties of the Kumaraswamy Distribution. Commun. Stat. Theory Methods, 2013,42(5): 741–755. https://doi.org/10.1080/03610926.2011.581782

[7] Garg, M.. On Distribution of Order Statistics from Kumaraswamy Distribution. Kyunpook Math. J., 2008, 48: 411–417. https://doi.org/10.5666/KMJ.2008.48.3.411

[8] Garg, M.. On Generalized Order Statistics from Kumaraswamy Distribution. Tamsui Oxford J. Math. Sci., 2009, 25(2): 153–166.

[9] Jones, M. C.. Kumaraswamy’s Distribution: A Beta-Type Distribution with Some Tractability Advantages. Stat. Method., 2009, 6(1): 70–81. https://doi.org/10.1016/j.stamet.2008.04.001

[10] Gholizadeh, A., Shirazi, M. A., Mosalmanzadeh, S.. Classical and Bayesian Estimation on Kumaraswamy Distribution Using Grouped and Un-Grouped Data Under Difference of Loss Functions. J. Appl. Sci., 2011, 11(12): 2154–2162, https://doi.org/10.3923/jas.2011.2154.2162

[11] Feroze N., El-Batal I.. Parameter Estimations Basedon Kumaraswamy Progressive Type II Censored Data with Random Removals. J. Mod. Appl. Stat. Methods, 2013, 12(2): 314–335. https://doi.org/10.22237/jmasm/1383279480

[12] Nadar, M., Papadopoulos, A., Kızılaslan, F.. Statistical Analysis for Kumaraswamy’s Distribution Based on Record Data. J. Stat. Pap., 2013, 54(2): 355–369. https://doi.org/10.1007/s00362-012-0432-7

[13] Kim, C., Jung, J., Chung, Y.. Bayesian Estimation for the Exponentiated Weibull Model Under Type II Progressive Censoring. Stat. Pap., 2011, 52(1): 53–70. https://doi.org/10.1007/s00362-009-0203-2

[14] Mahmoud, M. A. W., EL-Sagheer, R. M., Soliman, A. A., Abd-Ellah, A. H.. Inferences of the Lifetime Performance Index with Lomax Distribution Based on Progressive Type II Censored Data. Econ. Quality Control, 2014, 29(1): 39–51. https://doi.org/10.1515/eqc-2014-0005

[15] Shanker, R., Shukla, K.K., Fesshaye, H.. On weighted lindley distribution and its applications to model lifetime data. Jacobs Journal of Biostatistics, 2016, 1(1): 002.

[16] Shanker, R., Shukla, K.K., Mishra, A.. A three-parameter weighted lindley distribution and its applications to model survival time. Statistics, 2017, 18(2): 291-310.

[17] Singh, S.K., Singh, U., Yadav, A., Viswkarma, P.K.. On the estimation of stress strength reliability parameter of inverted exponential distribution. International Journal of Scientific World, 2015, 3(1): 98- 112.

[18] Sharma, V.K., Singh, S.K., Singh, U., Agiwal, V.. The inverse lindley distribution: A stress-strength reliability model. arXiv: 1405.6268, 2014.

[19] Efron, B.. Logistic regression, survival analysis and the kaplan-meier curve. Journal of the American Statistical Association, 1988, 83(402): 414-425.

Downloads

How to Cite

Ulubekova, F., & Ozel, G. (2020). Alpha Power-Kumaraswamy Distribution with An Application on Survival Times of Cancer Patients. Journal of Computer Science Research, 2(2), 30–36. https://doi.org/10.30564/jcsr.v2i2.1855

Issue

Vol. 2 , Iss. 2 (April 2020)

Article Type

Article

License

Copyright © 2020 Author(s)

Creative Commons License

This is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.

Crossref
Scopus
Google Scholar
Europe PMC