In this paper, We propose a new lifetime distribution with more flexibility called the New Cubic Transmuted Burr XII (NCTBXII) distribution. develop the proposed distribution on the basis of the cubic ranking transmutation map proposed by Granzotto et al. [1] . The distributional properties as (rth) moment, moment generating function, Characteristic function, reliability function and hazard rate are discussed for the proposed distribution. We derive representation for the order statistics.The maximum likelihood estimation of the model parameters is described. Applications of the proposed model and their fit are illustrated with data set and the corresponding diagnostic analyses are also provided.
REFERENCES
1.
D.
Granzotto
, F.
Louzada
, and N.
Balakrishnan
, “Cubic rank transmuted distributions: inferential issues and applications
,” Journal of statistical Computation and Simulation
, Vol. 87
, No. 14
, pp. 2760
–2778
, 2017
.2.
W. T.
Shaw
and I. R.
Buckley
, “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, 2009
.3.
A.
Afify
, H.
Yousof
, and S.
Nadarajah
, “The beta transmuted-h family for lifetime data
,” Statistics and its Interface
, Vol. 10
, No. 3
, pp. 505
–520
, 2017
.4.
K. A.
AL-Kadim
and M. H.
Mohammed
, “The cubic transmuted weibull distribution
,” Journal of University of Babylon
, Vol. 3
, pp. 862
–876
, 2017
.5.
M. M.
Rahman
, B.
Al-Zahrani
, and M. Q.
Shahbaz
, “A general transmuted family of distributions
,” Pakistan Journal of Statistics and Operation Research
, pp. 451
–469
, 2018
.6.
B.
Saraçoğlu
and C.
Tanış
, “A new statistical distribution: cubic rank transmuted kumaraswamy distribution and its properties
,” Journal of the National Science Foundation of Sri Lanka
, Vol. 46
, No. 4
, pp. 505
–18
, 2018
.7.
M. I.
Riffi
, “Higher rank transmuted families of distributions
,” IUG Journal of Natural Studies
, vol. 27
, No. 2
, 2019
.8.
M. M.
Rahman
, B.
Al-Zahrani
, and M. Q.
Shahbaz
, “Cubic transmuted weibull distribution: properties and applications
,” Annals of Data Science
, Vol. 6
, No. 1
, pp. 83
–102
, 2019
.9.
I. W.
Burr
, “Cumulative frequency functions
,” The Annals of mathematical statistics
, Vol. 13
, No. 2
, pp. 215
–232
, 1942
.10.
R. K.
Maurya
, Y. M.
Tripathi
, and M. K.
Rastogi
, “Transmuted burr xii distribution
,” Journal of the Indian Society for Probability and Statistics
, Vol. 18
, No. 2
, pp. 177
–193
, 2017
.11.
S.
Akter
, M. A. I.
Khan
, M. S.
Rana
, and M. M.
Rahman
, “Cubic transmuted burr-xii distribution with properties and applications
,” 2020
.12.
P. R.
Tadikamalla
, “A look at the burr and related distributions
,” International Statistical Review/Revue Internationale de Statistique
, pp. 337
–344
, 1980
.13.
R. N.
Rodriguez
, “A guide to the burr type xii distributions
,” Biometrika
, Vol. 64
, No. 1
, pp. 129
–134
, 1977
.14.
M. M.
Rahman
, B.
Al-Zahrani
, and M. Q.
Shahbaz
, “New general transmuted family of distributions with applications
,” Pakistan Journal of Statistics and Operation Research
, pp. 807
–829
, 2018
.15.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Table of integrals, series, and products. Academic press
, 2014
.16.
I.
Abdul-Moniem
and M.
Seham
, “Transmuted gompertz distribution
,” Computational and Applied Mathematics Journal
, Vol. 1
, No. 3
, pp. 88
–96
, 2015
.17.
R.
Barlow
, R.
Toland
, and T.
Freeman
, “A bayesian analysis of stress-rupture life of kevlar 49/epoxy spherical pressure vessels
,” in Proc. Conference on Applications of Statistics
’, Marcel Dekker
, New York
, 1984
.
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