Cubic Transmuted Power Function Distribution

Abstract

In statistics, it is always desired to generate new distributions in order to get more flexible real lifetime data fitting. The literature is rich of studies that aim to introducing new probability models and still growing rapidly. A few expansions of some outstanding lifetime disseminations have been created since last two decades for demonstrating and examinations numerous kinds of genuine information that having diverse arbitrary nature. In the present paper, a new family of transmuted distribution function, the cubic transmuted power function distribution (CTPFD), is introduced. Explicit formulae for its probability density function and cumulative distribution function are written. The statistical properties and some descriptive measures are studied. The moment matching estimation and maximum likelihood estimation for estimating the unknown distribution parameters are used. The properties of the estimators (biases, mean squared errors, and confidence intervals) are investigated via Monte Carlo simulation analysis. Three data sets have been considered for investigating the usefulness of CTPFD and have observed that our proposed distribution performs better than other probability models used in the analysis.

Keywords

• Power density function,Cubic transmuted distribution,Order statistic,Reliability function,Moment generating function

References

1. Afify AZ, Cordeiro GM, Ortega EMM, Yousof HM, Butt NS (2018). “The four-parameter Burr XII distribution: Properties, regression model, and applications.” Communications in Statistics - Theory and Methods, 47(11), 2605–2624.
2. Ahmad A, Akhter AS (2016). “Kurtosis Statistics with Reference to Power Function Distribution.” Journal of Statistics, 23, 123–140.
3. AL-Kadim KA, Mohammed MH (2017).“The cubic transmuted Weibull distribution.” Journal of University of Babylon for Pure and Applied Sciences, 25(3), 862–876.
4. Aryal GR, Tsokos CP (2009). “On the transmuted extreme value distribution with application.” Nonlinear Analysis: Theory, Methods & Applications, 71(12), 1401–1407.
5. Azzalini A (1985). “A class of distributions which includes the normal ones.” Scandinavian Journal of Statistics, 12, 171–178.
6. Bazyari A, Samuh MH (2018). “Two New Lifetime Distributions of X - Weibull Family: Theories and Applications.” Journal of Statistical Theory and Applications, 17(2), 375– 392.
7. Elal-Olivero D (2010). “Alpha-skew-normal distribution.” Proyecciones Journal of Mathematics, 29, 224–140.
8. Elbatal I (2013). “Transmuted Generalized Inverted Exponential Distribution.” Economic Quality Control, 28, 125–133.

9. Granzotto DCT, Louzada F, Balakrishnan N (2017). “Cubic rank transmuted distributions: inferential issues and applications.” Journal of Statistical Computation and Simulation, 87(14), 2760–2778.
10. Gupta R, Gupta R (2004). “Generalized skew-normal model.” Test, 13, 501–524.
11. Haq M, Butt N, Usman R, Fattah A (2016). “Transmuted Power Function Distribution.” Gazi University Journal of Science, 29, 177–185.
12. Jamalizadeh A, Behboodian J, Balakrishnan N (2008). “A two-parameter generalized skew- normal distribution.” Statistical and Probability Letters, 78, 1722–1728.
13. Meniconi M, Barry DM (1996). “The power function distribution: A useful and simple distribution to assess electrical component reliability.” Microelectronics Reliability, 36(9), 1207–1212.
14. Merovci F (2013). “Transmuted Rayleigh Distribution.” Austrian Journal of Statistics, 42, 21–31.
15. Oguntunde P, Adejumo O (2015). “The Transmuted Inverse Exponential Distribution.” International Journal of Advanced Statistics and Probability, 3, 1–7.
16. R Core Team (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
17. Rahman MM, Al-Zahrani B, Shahbaz MQ (2018). “A General Transmuted Family of Distributions.” Pakistan Journal of Statistics and Operation Research, 14(2), 451–469.
18. Shahzad MN, Asghar Z (2016). “Transmuted power function distribution: A more flexible distribution.” Journal of Statistics and Management Systems, 19(4), 519–539.
19. Sharafi M, Behboodian J (2008). “The Balakrishnan skew-normal density.” Statistical Papers, 49, 769–778.
20. Sharafi M, Sajjadnia Z, Behboodian J (2017). “A new generalization of alpha-skew-normal distribution.” Communications in Statistics - Theory and Methods, 46, 6098–6111.
21. Shaw W, Buckley I (2009). “The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map.” arXiv preprint arXiv:0901.0434.
22. Smith RL, Naylor JC (1987). “A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution.” Journal of the Royal Statistical Society. Series C (Applied Statistics), 36(3), 358–369.
23. Zaka A, Akhter AS (2014). “Modified Moment, Maximum Likelihood and Percentile Estimators for the Parameters of the Power Function Distribution.” Pakistan Journal of Statistics and Operation Research, 10(4), 369–388.