On the relationships between cubic transmutations and the mixture of failure distributions of k-out-of-3 systems

[1] K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), no. 1, 35–42.

[2] A. Akinsete, F. Famoye, and C. Lee, The beta-pareto distribution, Statistics 42 (2008), no. 6, 547–563.

[3] M. Alizadeh, F. Merovci, and G.G. Hamedani, Generalized transmuted family of distributions: Properties and applications, Hacettepe J. Math. Statist. 46 (2017), no. 4, 645–647.

[4] S.K. Ashour and M.A. Eltehiwy, Transmuted exponentiated Lomax distribution, Aust. J. Basic Appl. Sci. 7 (2013), no. 7, 658–667.

[5] M. Bourguignon, R.B. Silva, L.M. Zea, and G.M. Cordeiro, The Kumaraswamy Pareto distribution, J. Statist. Theory Appl. 12 (2013), no. 2, 129–144.

[6] V. Choulakian and M.A. Stephens, Goodness-of-fit tests for the generalized Pareto distribution, Technometrics 43 (2001), no. 4, 478–484.

[7] K.K. Das and L. Barman, On some generalized transmuted distributions, Int. J. Sci. Eng. Res 6 (2015), 1686–1691.

[8] A. El Hady and N. Ebraheim, Exponentiated transmuted Weibull distribution: A generalization of the Weibull distribution, Int. J. Math. Comput. Phys. Electric. Comput. Engin. 8 (2014), no. 6, 903–911.

[9] M. Eltehiwy and S. Ashour, Transmuted exponentiated modified Weibull distribution, Int. J. Basic Appl. Sci. 2 (2013), no. 3, 258–269.

[10] S. Eryilmaz, Computing reliability indices of repairable systems via signature, J. Comput. Appl. Math. 260 (2014), 229 – 235.

[11] C. Franko, M. Ozkut, and C. Kan, Reliability of coherent systems with a single cold standby component, J. Comput. Appl. Math. 281 (2015), 230 – 238.

[12] D.C.T. Granzotto, F. Louzada, and N. Balakrishnan, Cubic rank transmuted distributions: Inferential issues and applications, J. Statist. Comput. Simul. 87 (2017), no. 14, 2760–2778.

[13] C. Kus, A new lifetime distribution, Comput. Statist. Data Anal. 51 (2007), no. 9, 4497–4509.

[14] B.A. Maguire, E.S. Pearson, and A.H.A. Wynn, The time intervals between industrial accidents, Biometrika 39 (1952), no. 1/2, 168–180.

[15] M.M. Mansour, M.A. Enayat, S.M. Hamed, and M.S. Mohamed, A new transmuted additive Weibull distribution based on a new method for adding a parameter to a family of distributions, Int. J. Appl. Math. Sci. 8 (2015), 31–51.

[16] M.M. Mansour and S.M. Mohamed, A new generalized of transmuted Lindley distribution, Appl. Math. Sci 9 (2015), 2729–2748.

[17] F. Merovci, Transmuted exponentiated exponential distribution, Math. Sci. Appl. E-Notes 1 (2013), no. 2, 112–122.

[18] F. Merovci and L. Puka, Transmuted Pareto distribution, Prob. Stat. Forum, vol. 7, 2014, pp. 1–11.

[19] S. Nasiru and A. Luguterah, The new Weibull-Pareto distribution, Pakistan J. Statist. Oper. Res. 11 (2015), no. 1, 103–114.

[20] Z.M. Nofal, A.Z. Afify, H.M. Yousof, and G.M. Cordeiro, The generalized transmuted-G family of distributions, Commun. Statist. Theory Meth. 46 (2017), no. 8, 4119–4136.

[21] Z.M. Nofal and Y.M. El Gebaly, The generalized transmuted Weibull distribution for lifetime data, Pakistan J. Statist. Oper. Res. 13 (2017), no. 2, 355–378.

[22] M.M. Rahman, B. Al-Zahrani, and M.Q. Shahbaz, A general transmuted family of distributions, Pakistan J. Statist. Oper. Res. 14 (2018), no. 2.

[23] A. Saboor, M. Nauman Khan, G.M. Cordeiro, M.A.R. Pascoa, P.L. Ramos, and M. Kamal, Some new results for the transmuted generalized gamma distribution, J. Comput. Appl. Math. 352 (2019), 165 – 180.

[24] W.T. Shaw and I.R.C. Buckley, The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions, Submitted, Feb 7 (2007), 64.

[25] W.T. Shaw and I.R.C. Buckley, The alchemy of probability distributions: Beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, ArXiv e-prints (2009).

[26] M.H. Tahir, G.M. Cordeiro, A. Alzaatreh, M. Mansoor, and M. Zubair, A new Weibull–Pareto Distribution: Properties and applications, Commun. Statist. Simul. Comput. 45 (2016), no. 10, 3548–3567.

[27] M. Yilmaz, M. Hameldarbandi, and S. Acik Kemaloglu, Exponential-modified discrete Lindley distribution, SpringerPlus 5 (2016), no. 1, 1660.

[28] M. Yilmaz, N. Potas, and B. Buyum, A classical approach to modeling of coal mine data, Chaos, Complexity and Leadership 2014, Springer, 2016, pp. 65–73.

[29] M. Yilmaz, N. Potas, and B. Topcu, Reliability properties of systems with three dependent components, Chaos, Complexity and Leadership 2013, Springer, 2015, pp. 117–127.