ON THE UTILITY OF [0,1]-VALUED CONTINUOUS LIFETIME DISTRIBUTIONS: A REVIEW

Authors

  • N.O Ubaka Department of Statistics, Federal University of Oye-Ekiti, Ekiti State, Nigeria Author
  • Friday Ewere Department of Statistics, Faculty of Physical Sciences, P.M.B. 1154, University of Benin, Benin City, Edo State, Nigeria Author

DOI:

https://doi.org/10.60787/tnamp-19-53-62

Keywords:

Beta Distribution, Continuous Bernoulli Distribution, Kumaraswamy Distribution, Lifetime Distribution

Abstract

Recent studies on the theory of statistical distribution reveal a wide application of continuous lifetime distributions with support [0,1] in real world data fittings. Bounded lifetime distributions such as Kumaraswamy distribution, Beta distribution, one-parameter Topp-Leone distribution and the recently developed continuous Bernoulli distribution have gained popularity in modelling real datasets taking the form of proportions, percentages, probabilities, etc.

Several attempts have been made to generalize these continuous lifetime distributions in order to increase their chance of providing good fit in real life data analysis. This paper presents a general review on the utility of [0,1]-valued lifetime distributions.

Downloads

Download data is not yet available.

Author Biography

  • Friday Ewere, Department of Statistics, Faculty of Physical Sciences, P.M.B. 1154, University of Benin, Benin City, Edo State, Nigeria

     

     

                                                                                                                                                                                          

References

Jambunathan, M. V. (1954). Some Properties of Beta and Gamma Distribution. The Annals of Mathematical Statistics, 25(2): 401-405.

Evans, M., Hasting, N., & Peacock, B. (2000). Beta distribution. Chapter 5 in Statistical Distribution. 3rd edition, New York; Wiley, 34-42.

Betkowski, M. and Pownuk, A. (2004). Calculating risk of cost using Monte Carlo Simulation with fuzzy parameters in Civil Engineering. In Proceeding of NSF Workshop on Reliability Engineering Computing, 179-192.

Price, A. L., Patterson,N. J., Plenge, R. M., Weinblatt, M. E., Shadick, N. A., & Reich, D. (2006). Principal Component Analysis corrects for stratification in genome-wide association studies. Nature Genetics, 38: 904-909.

Kuhl, M. E., Ivy, J. S., Lada, E. K., Steiger, N. M., Wagner, M. A., & Wilson, J. R. (2010). Univariate Input Models for Stochastic Simulation. Journal of Simulations. Vol.4: 81-97.

Eugene, N., Lee, C. and Famoye, F. (2002). The beta-normal distribution and its applications.Communications in Statistics - Theory and Methods, 31(4): 497-512.

Nadarajah, S. and Kotz, S. (2004). The Beta Gumbel Distribution. Mathematical Problems in Engineering, 323–332.http://dx.doi.org/10.1155/S1024123X04403068

Famoye, F., Lee, C. and Olumolade, O, (2005). The Beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2): 121-136.

Nadarajah, S. and Kotz, S. (2006). The Beta Exponential Distribution. ReliabilityEngineeringSystemSafety, 91: 689–697

Akinsete, A., Famoye, F. and Lee, C. (2008). The Beta-Pareto distribution. Statistics, 42: 547-563.

Silva, G.O., Ortega, E.M.M. and Cordeiro, G.M. (2010). The beta modified Weibull distribution. Lifetime Data Analysis,16, 409-430.

Cordeiro, G. M.and de Castro, M. (2011). A new family of generalized distributions.

Journal of Statistical Computation and Simulation. 81: 883-898.

Cordeiro, G. M. and dos Santos Brito, R. (2012). The Beta Power Distribution. Brazilian Journal of Probability and Statistics, 26(1): 88-112.

Adepoju, K. A., Chukwu, A.U. and Wang, M. (2014). The Beta Power Exponential Distribution. Journal of Statistical Science and Application, 2: 37-46.

Rodrigues, J.A., Silva, A. P. C. M, and Hamedani, G. G., (2015). The Beta Exponentiated Lindley Distribution. Journal of Statistical Theory and Applications, 14(1): 60-75.

Pararai M., Waharena-Liyanage, G. and Oluyede, B. O. (2015a). A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data. Theoretical Mathematics and Applications, 5(1): 53-96.

MirMostafaee, S.M.T.K., Mahdizadeh, M. and Nadarajah, S. (2015). The Beta Lindley Distribution. Journal of Data Science, 13: 603-626.

Saboor, A., Bakouch, H. S. and Khan, M. N. (2016). BetaSarhan-Zaindin modified Weibulldistribution.Applied Mathematical Modelling,doi:10.1016/j.apm.2016.01.033

Mead, M.E., Afify, A.Z., Hamedani, G.G. and Ghosh, I. (2017). The BetaExponentialFrechet Distribution with Applications. AustrianJournal of Statistics, 46: 41-63. http://www.ajs. or.at/doi:10.17713/ajs.v46i1.144.

Badr, M. M. (2019). Beta Generalized Exponentiated-Frechet Distribution Application. Open Physics, 17:687–697. https://doi.org/10.1515/phys-2019-0071

Shahzad, M. N., Ullah, E. and Hussanan, A.(2019). Beta Exponentiated Modified Weibul l Distribution. Symmetry, 11, 781. doi:10.3390/sym11060781

Opone, F. C. and Ekhosuehi, N (2017). A Study on the moments and performance of the maximum likelihood estimates (mle) of the Beta distribution. Abacus (Mathematics Science Series), 44(2), 148-154.

Kumaraswamy, P. (1980). A Generalized Probability Density Function for Doubly Bounded Random Process. Journal of Hydrology. 46, 79-88.

Jones, M. C. (2009). Kumaraswamy’s Distribution: A Beta-Type Distribution with Some Tractability Advantages. Statistical Methodology. 6, 70-81.

Cordeiro, G. M., Ortega, E. M. M., Nadarajah, S. (2010). The KumaraswamyWeibull distribution with applicationto failure data. Journal of the Franklin Institute, 347:1399–1429.

Pascoa, M. A. R., Ortega, E. M. M. and Cordeiro, G. M. (2010). The Kumaraswamy generalized gamma distribution withapplication in survival analysis. Statistical Methodology, 8: 411–433

Cordeiro, G.M., Nadarajah, S. and Ortega, E.M.M. (2012). The KumaraswamyGumbel distribution. Statistical Methodsand Applications, 21: 139-168.

Shahbaz, Q. M., Shahbaz, S. and Butt, N. S. (2012). The Kumaraswamy–Inverse Weibull Distribution. Pakistan Journal of Statistics and Operation Research, 8(3): 479-489

Paranaiba, P. F., Ortega, E. M., Cordeiro, G. M., and de Pascoa, M. A. (2012). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 1-27.DOI:10.1080/00949655.2012.683003

Elbatal, I. and Elgarhy, M. (2013). Statistical Properties of Kumaraswamy Quasi Lindley Distribution. International Journal of Mathematics Trends and Technology, 4(10): 237-246.

Bourguignon, M., Silva, R. B., Zea, M. L. and Cordeiro, G. M. (2012). The Kumaraswamy Pareto distribution. Journal of Statistical Theory and Applications, 12(2): 129-144.

El-Sherpieny, E. A. and Ahmed, M. A. (2014). On the Kumaraswamy-Kumaraswamy distribution. International Journal of Basic and AppliedSciences, 3(4):372-381.

Pararai, M., Oluyede, B. O. and Warahena-Liyanage, G. (2015b). Kumaraswamy Lindley-Poisson Distribution: Theory and Applications. Asian Journal of Mathematics and Applications. (article ID ama0261), 1-30.

Oluyede, B. O., Yang, T. and Makubate, B. (2016). A New Class of Generalized Power Lindley Distribution with Application to Lifetime Data. Asian Journal of mathematicsand applications, (Article ID ama0279): 1-34

Behairy, S. M., AL-Dayian, G. R. and EL-Helbawy, A. A. (2016). The Kumaraswamy-Burr Type III Distribution: Properties andEstimation. British Journal of Mathematics & Computer Science, 14(2): 1-21

Salem, M. H. and Hagag, E. A. (2017). Mathematical properties of the Kumaraswamy-Lindley distribution and its applications. International Journal of Advanced Statistics and Probability,5(1): 17-22.

Akata, I. U.,Opone, F. C.andOsagiede, F.E.U. (2023). The Kumaraswamy Unit-Gompertz Distribution and Its Application to Lifetime Dataset. Earthline Journal of Mathematical Sciences, 11(1): 1-22.

Topp, C. W., and Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50: 209-219.

Sangsanit Y., and Bodhisuwan, W. (2016). The Topp-Leone generator of distributions: properties and inferences.Songklanakarin Journal of Science and Technology, 38: 537-548.

Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S. and Shahbaz, M. Q. (2016). Topp-Leone family of distributions: Some properties and application. Pakistan Journal Statistics and Operation Research, 12 (3): 443-451.

Bodhisuwan, W. (2016). The Topp-Leone Gumbel Distribution. 12th International Conference on Mathematics, Statistics, and their Applications (ICMSA), Banda Aceh, Indonesia. 93-98.

Aryal, G. R., Ortega, E. M., Hamedani, G. G., and Yousof, H. M. (2017). The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications. International Journal of Statistics and Probability, 6(1): 126-141.

Reyad, M. H., and Othman, S. A. (2017). The Topp-Leone Burr-XII Distribution: Properties

and Applications. British Journal of Mathematics & Computer Science, 21(5): 1-15.

Yousof, M. H. and Korkmaz, C. M. (2017). Topp-Leone Nadarajah-Haghighi distribution. Journal of Statisticians: Statistics and Actuarial Sciences, 2: 119-128.

Abbas, S., Taqi, S. A, Mustafa, F., Murtaza, M., and Shahbaz, M. Q. (2017). Topp-Leone Inverse Weibull Distribution: Theory andApplication. European Journal of Pure and Applied Mathematics, 10(5): 1005-1022.

Aryuyuen, S. (2018). A Topp-Leone Generator of Exponentiated Power Lindley Distribution and Its Application. Applied Mathematical Sciences, 12(12): 567 - 579.

Sharma, K. V. (2018). Topp–Leone normal distribution with application to increasing failure rate data. Journal of Statistical Computation and Simulation, DOI: 10.1080/00949655.2018.1447574.

Atem, B. A. M., Nasiru, S. and Nantomah, K. (2018). Topp-Leone Linear Exponential Distribution. Stochastics and Quality Control. https://doi.org/10.1515/eqc-2017-0022.

Tuoyo, D., Opone, F. C. and Ekhosuehi, N. (2021). The Topp-Leone Weibull Distribution: Its Properties and Application to Lifetime Data. Earthline Journal of Mathematical Sciences, 7 (2): 381-401.

Loaiza-Ganem, G. and Cunningham, J.P. (2019). The continuous bernoulli: fixing a pervasiveerror in variationalautoencoders. In Advances in Neural Information Processing Systems,13266-13276.

Wang, K. and Lee, M. (2020). Continuous Bernoulli distribution: simulator and test statistic.DOI: 10.13140/RG.2.2.28869.27365

Chesneau, C., Opone, F. C. and Ubaka, N. (2022). Theory and applications of the transmuted continuous Bernoulli distribution. Earthline Journal of Mathematical Sciences, 10(2): 385-407.

Shaw, W. and Buckley, I. (2009). The alchemy of probability distributions: beyond Gram- Charlier expansions and a skew- kurtoticnormal distribution from a rank transmutation map. arXivprereprint, arXiv, 0901.0434.

Downloads

Published

2024-03-29

How to Cite

ON THE UTILITY OF [0,1]-VALUED CONTINUOUS LIFETIME DISTRIBUTIONS: A REVIEW. (2024). The Transactions of the Nigerian Association of Mathematical Physics, 19, 53-62. https://doi.org/10.60787/tnamp-19-53-62

Share

Similar Articles

1-10 of 11

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