Document Zbl 1426.62048

Chhetri, Sher B.; Akinsete, Alfred A.; Aryal, Gokarna; Long, Hongwei

The Kumaraswamy transmuted Pareto distribution. (English) Zbl 1426.62048

J. Stat. Distrib. Appl. 4, Paper No. 11, 24 p. (2017).

Summary: In this work, a new five-parameter Kumaraswamy transmuted Pareto (KwTP) distribution is introduced and studied. We discuss various mathematical and statistical properties of the distribution including obtaining expressions for the moments, quantiles, mean deviations, skewness, kurtosis, reliability and order statistics. The estimation of the model parameters is performed by the method of maximum likelihood. We compare the distribution with few other distributions to show its versatility in modeling data with heavy tail.

Cited in 2 Documents

MSC:

62E10	Characterization and structure theory of statistical distributions
62E15	Exact distribution theory in statistics

Keywords:

Kumaraswamy distribution; quadratic rank transmutation map (QRTM); Pareto distribution; hazard function; maximum likelihood estimation

Software:

AdequacyModel

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References:

[1]	Afify, AZ, Cordeiro, GM, Yousof, HM, Alzaatreh, A, Nofal, ZM: The Kumaraswamy transmuted-g family of distributions: Properties and applications. J. Data Sci. 14, 245-270 (2016).
[2]	Afify, AZ, Nofal, ZM, Butt, NS: Transmuted complementary Weibull geometric distribution. Pak. J. Stat. Oper. Res.4, 435-454 (2014). · Zbl 1509.62134 · doi:10.18187/pjsor.v10i4.836
[3]	Akinsete, A, Famoye, F, Lee, C: The beta-Pareto distributions. Statistics. 42(6), 547-563 (2008). · Zbl 1274.60033 · doi:10.1080/02331880801983876
[4]	Akinsete, AA, Famoye, F, Lee, C: The Kumaraswamy - geometric distribution. J. Stat. Distrib. Appl. 1, 1-21 (2014). · Zbl 1357.62068 · doi:10.1186/s40488-014-0017-1
[5]	Aryal, GR, Tsokos, CP: On the transmuted extreme value distribution with application. Nonlinear Anal. Theory Methods and Appl. 7, 1401-1407 (2009). · Zbl 1238.60018 · doi:10.1016/j.na.2009.01.168
[6]	Aryal, GR, Tsokos, CP: Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Eur. J. Pur. Appl. Math. 2(2), 89-102 (2011). · Zbl 1389.62150
[7]	Ashour, SK, Eltehiwy, MA: Transmuted Lomax distribution. Am. J. Appl. Math. Stat. 1(6), 121-127 (2013). · doi:10.12691/ajams-1-6-3
[8]	Bourguignon, MB, Silva, RB, Zea, LM, Cordeiro, GM: The Kumaraswamy Pareto distribution. J. Stat. Theory Appl. 12(2), 129-144 (2013). · doi:10.2991/jsta.2013.12.2.1
[9]	Bowley, AL: Elements of Statistics. 4th edn. Charles Scribner, New York, NY (1920). · JFM 48.0616.06
[10]	Chhetri, S, Long, H, Aryal, G: The beta transmuted Pareto distribution: Theory and applications. J. Stat. Appl. Prob. 6(2), 243-258 (2017). · doi:10.18576/jsap/060201
[11]	Choulakian, V, Stephens, MA: Goodness-of-fit for the generalized Pareto distribution. Technometrics. 43, 478-484 (2001). · doi:10.1198/00401700152672573
[12]	Cordeiro, GM, de Castro, M: A new family of generalized distributions. J. Stat. Comput. Simul. 81, 883-898 (2011). · Zbl 1219.62022 · doi:10.1080/00949650903530745
[13]	Cordeiro, GM, Ortega, EMM, Nadarajah, S: The Kumaraswamy Weibull distribution with application to failure data. J. Frankl. Inst. 347, 1399-1429 (2010). · Zbl 1202.62018 · doi:10.1016/j.jfranklin.2010.06.010
[14]	de Pascoa, MAR, Ortega, EMM, Cordeiro, GM: The Kumaraswamy generalized gamma distribution with application in survival analysis. Stat Methodol. 8, 411-433 (2011). · Zbl 1219.62026 · doi:10.1016/j.stamet.2011.04.001
[15]	Elbatal, I: The Kumaraswamy exponentiated Pareto distribution. Econ. Qual. Control. 28(1), 1-8 (2013). · Zbl 1296.62033 · doi:10.1515/eqc-2013-0006
[16]	Eugene, N, Lee, C, Famoye, F: The beta-normal distribution and its applications. Commun. Stat. Theory Methods. 31, 497-512 (2002). · Zbl 1009.62516 · doi:10.1081/STA-120003130
[17]	Gradshteyn, IS, Ryzhik, IM: Table of Integrals, Series, and Products. 3rd edn. Academic Press, New York (2000). · Zbl 0981.65001
[18]	Hady, AE, Ebraheim, N: Exponentiated transmuted Weibull distribution: A generalization of the Weibull distribution. Int. Sch. Sci. Res. Innov. 8(6), 903-911 (2014).
[19]	Hussian, MA: Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution. Appl. Math. Sci. 8(27), 1297-1310 (2014).
[20]	Jones, MC: Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Stat Methodol. 6(1), 70-81 (2009). · Zbl 1215.60010 · doi:10.1016/j.stamet.2008.04.001
[21]	Kenny, JF, Keeping, ES: Mathematics of Statistics. 3rd edn. D. Van Nostrand Co., New Jersey (1962).
[22]	Khan, MS, King, R: Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Eur. J. Pur. Appl. Math. 6(1), 66-88 (2013). · Zbl 1389.90103
[23]	Khan, MS, King, R, Hudson, IL: Transmuted Kumaraswamy distribution. Stat. Transit. 17(2), 183-210 (2016).
[24]	Kumaraswamy, P: A generalized probability density function for double-bounded random processes. Hydrology. 46, 79-88 (1980). · doi:10.1016/0022-1694(80)90036-0
[25]	Marinho, PRD, Bourguignon, M, Dias, CRB: R Package - Adequacymodel (2016). https://cran.r-project.org/web/packages/AdequacyModel/AdequacyModel.pdf.
[26]	Mdziniso, NC, Cooray, K: Odd Pareto families of distributions for modelling loss payment data. Scand. Actuar. J.1-22 (2017). http://dx.doi.org/10.1080/03461238.2017.1280527. · Zbl 1416.91208
[27]	Merovci, F, Puka, L: Transmuted Pareto distribution. ProbStat Forum. 07, 1-11 (2014). · Zbl 1284.62102
[28]	Moors, JJA: A quantile alternative for kurtosis. J. R. Stat. Series D Stat. 37(1), 25-32 (1988).
[29]	Nadarajah, S: Exponentiated Pareto distribution. Stat. J. Theor. Appl. Stat. 39(3), 255-260 (2005). · Zbl 1070.62008
[30]	Owokolo, EA, Oguntade, PE, Adejumo, AO: Performance rating of the transmuted exponential distribution: an analytical approach. SpringerPlus. 4, 818 (2015). doi:10.1186/s40064-015-1590-6. · doi:10.1186/s40064-015-1590-6
[31]	Saulo, H: The Kumaraswamy Birnbaum-Saunders distribution. J. Stat. Theory Pract. 6(4), 745-759 (2012). · Zbl 1430.62040 · doi:10.1080/15598608.2012.719814
[32]	Shams, TM: The Kumaraswamy-generalized Lomax distribution. Middle East J. Sci. Res. 17(5), 641-646 (2013).
[33]	Shaw, WT, Buckley, IRC: The alchemy of probability distributions: beyond Gram-Charlier & Cornish-Fisher expansions, and skew-normal or kurtotic-normal distributions. Conference on Computational Finance, IMA, 6670 (2007). Research Report.
[34]	Shaw, WT, Buckley, IRC: The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Conference on Computational Finance, IMA, 0901-0434 (2009). Research Report.
[35]	Tahir, MH, Cordeiro, GM: Compounding of distributions: a survey and new generalized classes. J. Stat. Distrib. Appl. 3, 183-210 (2016). · Zbl 1375.60050 · doi:10.1186/s40488-016-0052-1
[36]	Yousof, HM, Afify, AZ, Alizadeh, M, Butt, NS, Hamedani, GG, Ali, MM: The transmuted exponentiated generalized-g family of distributions. Pak. J. Stat. Oper. Res.4, 441-464 (2015). · Zbl 1509.60068 · doi:10.18187/pjsor.v11i4.1164

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