A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling

Subrata Chakraburty; Morad Alizadeh; Laba Handique; Emrah Altun; G. G. Hamedani

doi:10.21307/stattrans-2021-039

A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling

Subrata Chakraburty Department of Statistics, Dibrugarh University, Dibrugarh-786004, India ORCID:https://orcid.org/0000-0002-6405-1486 , Morad Alizadeh Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 75169, Iran ORCID:https://orcid.org/0000-0001-6638-2185 , Laba Handique Department of Mathematics and Statistics, Golaghat Commerce College, Dibrugarh University, India ORCID:https://orcid.org/0000-0001-9255-2918 , Emrah Altun Department of Mathematics, Bartin University, Bartin 74100, Turkey ORCID:https://orcid.org/0000-0001-5065-2523 , G. G. Hamedani Department of Mathematical and Statistical Sciences Marquette University, USA, USA ORCID:https://orcid.org/0000-0001-7976-1088 Statistics in Transition new series, vol. 22, 2021, 4, pages: 77-100 Published online: 8 December 2021 DOI 10.21307/stattrans-2021-039

1237 Views 36 Downloads

ARTICLE

(English) PDF

ABSTRACT

The paper proposes a new family of continuous distributions called the extended odd half Cauchy-G. It is based on the T-X construction of Alzaatreh et al. (2013) by considering half Cauchy distribution for T and the exponentiated G(x;ξ) as the distribution of X. Several particular cases are outlined and a number of important statistical characteristics of this family are investigated. Parameter estimation via several methods, including maximum likelihood, is discussed and followed up with simulation experiments aiming to asses their performances. Real life applications of modeling two data sets are presented to demonstrate the advantage of the proposed family of distributions over selected existing ones. Finally, a new regression model is proposed and its application in modeling data in the presence of covariates is presented.

KEYWORDS

T-X method; regression; simulation; estimation

REFERENCES

Aarset, M. V., (1987). How to identify bathtub hazard rate, IEEE Transactions on Reliability, 36, pp. 106–108.

Alzaatreh, A., Lee, C. and Famoye, F., (2013). A new method for generating families of continuous distributions. Metron, 71, pp. 63–79.

Anderson, T.W. and Darling, D. A., (1952). Asymptotic theory of certain "goodness-of-fit" criteria based on stochastic processes. Ann Math Stat, 23, pp. 93–212.

Arwa, Y., Al- Saiari, Lamya, A., Baharith and Salwa, Mousa A., (2014). Marshall-Olkin extended Burr type XII distribution. International Journal of Statistics and Probability, 3, pp. 78–84.

Bjerkedal, T., (1960). Acquisition of resistance in Guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72, pp. 130–148.

Burr, I. W., (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13, pp. 215–232.

Choi, K. and Bulgren,W. G., (1968). An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society: Series B (Methodological), 30, pp. 444–460.

Cordeiro, G. M., Alizadeh, M., Ramires, T. G. and Ortega, E. M. M., (2017). The generalized odd half-Cauchy family of distributions: Properties and applications. Communications in Statistics-Theory and Methods, 46, pp. 5685–5705.

Dey, S., Mazucheli, J. and Nadarajah, S., (2018). Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 37, pp. 2094–2111.

Fleming, T. R. and Harrington, D. P., (1994). Counting process and survival analysis, John Wiley, New York.

Gradshteyn, I. S. and Ryzhik, I .M., (2007). Tables of Integrals, Series, and Products, Academic Press, New York.

Hesham, M. R. and Soha, A. O., (2017). The Topp-Leone Burr-XII distribution: Properties and applications. British Journal of Mathematics and Computer Science, 21, pp. 1–15.

Hinkley, D., (1977). On quick choice of power transformations. Journal of the Royal Statistical Society, Series (c), Applied Statistics, 26, pp. 67–69.

Korkmaz, M., Ç., Altun, E., Yousof, H. M. and Hamedani, G. G. (2020). The Hjorth’s IDB Generator of Distributions: Properties, Characterizations, Regression Modeling and Applications. Journal of Statistical Theory and Applications, 19(1), pp. 59–74.

Macdonald, P. D. M., (1971). Comment on "An estimation procedure for mixtures of distributions" by Choi and Bulgren. J R Stat Soc B, 33, pp. 326–329.

Mead, M. E., (2014). A new generalization of Burr XII distribution. Journal of Statistics: Advances in Theory and Applications, 12, pp. 53–71.

Paranaíba, P. F., Ortega, E. M. M., Cordeiro, G. M. and Pescim, R. R., (2011). The beta Burr XII distribution with application to lifetime data. Computational Statistics and Data Analysis, 55, pp. 1118–1136.

Paranaíba, P. F., Ortega, E. M. M., Cordeiro, G. M. and de Pascoa, M. A. R., (2013). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 83, pp. 2117–2143.

Shibu, D. S. and Irshad, M. R., (2016). Extended new generalized Lindley Distribution . Statistica, 76, pp. 41–55.

Swain, J., Venkatraman, S. and Wilson, J., (1988). Least squares estimation of distribution function in Johnson’s translation system. Journal of Statistical Computation and Simulation, 29, pp. 271–297.

Therneau, T. M., Grambsch, P. M. and Fleming, T. R., (1990). Martingale-based residuals for survival models. Biometrika, 77, pp. 147–160.

Yousof, H. M., Altun, E. and Hamedani, G. G., (2018). A new extension of Fréchet distribution with regression models, residual analysis and characterizations. Journal of Data Science, 16(4), pp. 743–770.