Startseite Mathematik A new kumaraswamy generalized family of distributions: Properties and applications
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

A new kumaraswamy generalized family of distributions: Properties and applications

  • Muhammad Adnan Hussain , Muhammad Hussain Tahir EMAIL logo und Gauss M. Cordeiro
Veröffentlicht/Copyright: 10. Dezember 2020
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 70 Heft 6

Abstract

The Kumaraswamy generalized family of distributions proposed by Cordeiro and de-Castro (2011), has received increased attention in modern distribution theory with 624 google citations, and more than 50 special models have been studied so far. We define another generator, and then propose a new Kumaraswamy generalized family of distributions by inducting this new generator. Some useful properties of the proposed family are obtained such as quantiles, linear representation of the density, moments and generating function. The method of maximum likelihood is used for estimating family parameters. The properties of a special model of the family, called new Kumaraswamy-Burr XII distribution, are reported. A simulation study is conducted to assess the performance of maximum likelihood estimates of the proposed model. Two real-life data sets are analyzed to illustrate the flexibility of proposed model.

Keywords: Burr-XII distribution; generalized family; Kumaraswamy-G family; maximum likelihood method; T-X family
MSC 2010: 62E15; 62E05; 62E10

Acknowledgement

The authors would like the thank two anonymous reviewers whose suggestions led to improvement in our manuscript.

References

[1] AFIFY, A. Z.―CORDEIRO, G. M.―ORTEGA, E. M. M.―YOUSOF, H. M.―BUTT, N. S.: The four-parameter Burr XII distribution: Properties, regression model, and applications Commun. Stat. Theory Methods 47 (2018), 2605-2624.10.1080/03610926.2016.1231821Suche in Google Scholar

[2] AL-AQTASH, R.―LEE, C.―FAMOYE, F.: Gumbel-Weibull distribution: Properties and applications J. Mod. Appl. Stat. Methods 13 (2014), 201-225.10.22237/jmasm/1414815000Suche in Google Scholar

[3] ALEXANDER, C.―CORDEIRO, G. M.―ORTEGA, E. M. M.―SARABIA, J. M.: Generalized beta-generated distributions Comput. Stat. Data Anal. 56 (2012), 1880-1897.10.1016/j.csda.2011.11.015Suche in Google Scholar

[4] ALIZADEH, M.―ALTUN, E.―CORDEIRO, G. M.―RASEKHI, M.: The odd power-Cauchy family of distributions: Properties, regression models and applications J. Stat. Comput. Simul. 88 (2018), 785-807.10.1080/00949655.2017.1406938Suche in Google Scholar

[5] ALZAATREH, A.―FAMOYE, F.―LEE, C.: A new method for generating families of continuous distributions Metron 71 (2013), 63-79.10.1007/s40300-013-0007-ySuche in Google Scholar

[6] AZZALINI, A.: A class of distributions which includes the normal ones Scand. J. Stat. 12 (1985), 171-78.Suche in Google Scholar

[7] BOURGUIGNON, M.―SILVA, R. B.―CORDEIRO, G. M.: The Weibull-G family of probability distributions J. Data Sci. 12 (2014), 53-68.10.6339/JDS.201401_12(1).0004Suche in Google Scholar

[8] COORA, K.―ANANDA, M. M. A.: A generalization of the half-normal distribution with applications to lifetime data Commun. Stat. Theory Methods 37 (2008), 1323-1337.10.1080/03610920701826088Suche in Google Scholar

[9] CORDEIRO, G. M.―DE-CASTRO, M.: A new family of generalized distributions J. Stat. Comput. Simul. 81 (2011), 883-898.10.1080/00949650903530745Suche in Google Scholar

[10] CORDEIRO, G. M.―ORTEGA, E. M. M.―CUNHA, D. C. C.: The exponentiated generalized class of distributions J. Data Sci. 11 (2013), 1-27.10.6339/JDS.2013.11(1).1086Suche in Google Scholar

[11] CORDEIRO, G. M.―ALIZADEH, M.―RAMIRES, T. G.―ORTEGA, E. M. M.: The generalized odd half-Cauchy family of distributions: Properties and applications Commun. Stat. Theory Methods 46 (2018), 5685{ 5705.10.1080/03610926.2015.1109665Suche in Google Scholar

[12] CORDEIRO, G. M.―YOUSOF, H. M.―RAMIRES, T. G.―ORTEGA, E. M. M.: The Burr XII system of densities: Properties, regression model and applications J. Stat. Comput. Simul. 88 (2018), 432-456.10.1080/00949655.2017.1392524Suche in Google Scholar

[13] DA SILVA, R. V.―GOMES{SILVA, F.―RAMOS, M. W. A.―CORDEIRO, G. M.: The exponentiated Burr XII Poisson distribution with application to lifetime data Int. J. Stat. Prob. 4 (2015), 112-131.10.5539/ijsp.v4n4p112Suche in Google Scholar

[14] EUGENE, N.―LEE, C.―FAMOYE, F.: Beta-normal distribution and its applications Commun. Stat. Theory Methods 31 (2002), 497-512.10.1081/STA-120003130Suche in Google Scholar

[15] GLEATON, J. U.―LYNCH, J. D.: Properties of generalized log-logistic families of lifetime distributions J. Probab. Stat. Sci. 4 (2006), 51-64.Suche in Google Scholar

[16] GUERRA, R. R.―PEÑA-RAMÍREZ, F. A.―PEÑA-RAMÍREZ, M. R.―CORDEIRO, G. M.: A note on the density expansion and generating function of the beta Burr XII Math. Methods Appl. Sci. 43 (2020), 1817-1824.10.1002/mma.6005Suche in Google Scholar

[17] GUERRA, R. R.―PEÑA-RAMÍREZ, F. A.―CORDEIRO, G. M.: The gamma Burr XII distributions: Theory and applications J. Data Sci. 15 (2017), 467-494.10.6339/JDS.201707_15(3).0006Suche in Google Scholar

[18] GUPTA, R. C.―GUPTA, P. L.―GUPTA, R. D.: Modeling failure time data by Lehman alternatives Commun. Stat. Theory Methods 27 (1998), 887-904.10.1080/03610929808832134Suche in Google Scholar

[19] HASSAN, A. S.―HEMEDA, S. E.: A new fmily of additive Weibull-generated distributions Int. J. Math. Appl. 4 (2017), 151-164.Suche in Google Scholar

[20] HASSAN, A. S.―NASSR, S. G.: Power Lindley-G family of distributions Ann. Data Sci. 6 (2019), 189-210.10.1007/s40745-018-0159-ySuche in Google Scholar

[21] KUMARASWAMY, P.: Generalized probability density function for double bounded random processes J. Hydrology 46 (1980), 79-88.10.1016/0022-1694(80)90036-0Suche in Google Scholar

[22] MAHDAVI, A.―KUNDU, D.: A new method for generating distributions with an application to exponential distribution Commun. Stat. Theory Methods 46 (2017), 6543-6557.10.1080/03610926.2015.1130839Suche in Google Scholar

[23] MAITI, S. S.―PRAMANIK, S.: A generalized Xgamma generator family of distributionshttps://arxiv.org/abs/1805.03892v1Suche in Google Scholar

[24] MARSHALL, A. W.―OLKIN, I.: A new method for adding parameters to a family of distributions with application to the exponential and Weibull families Biometrika 84 (1997), 641-652.10.1093/biomet/84.3.641Suche in Google Scholar

[25] PARANAÍBA, P. F.―ORTEGA, E. M. M.―CORDEIRO, G. M.―DE-PASCOA, M. A. R.: The Kumaraswamy Burr XII distribution: theory and practice J. Stat. Comput. Simul. 83 (2013), 2117-2143.10.1080/00949655.2012.683003Suche in Google Scholar

[26] PARANAÍBA, P. F.―ORTEGA, E. M. M.―CORDEIRO, G. M.―PESCIM, R. R.: The beta Burr XII distribution with application to lifetime data Comput. Stat. Data Anal. 55 (2011), 1118-1136.10.1016/j.csda.2010.09.009Suche in Google Scholar

[27] RISTIĆ, M. M.―BALAKRISHNAN, N.: The gamma-exponentiated exponential distribution J. Stat. Comput. Simul. 82 (2012), 1191-1206.10.1080/00949655.2011.574633Suche in Google Scholar

[28] SHAW, W. T.―BUCKLEY, I. R.: The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map UCL discovery repository, 2007, http://discovery.ucl.ac.uk/id/eprint/643923Suche in Google Scholar

[29] SILVA, F. S.―PERCONTINI, A.―DE-BRITO, E.―RAMOS, M. W.―VENANCIO, R.―CORDEIRO, G. M.: The odd Lindley-G family of distribution Aust. J. Stat. 46 (2017), 65-87.10.17713/ajs.v46i1.222Suche in Google Scholar

[30] SMITH, R. L.―NAYLOR, J. C.: A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution J. Appl. Stat. 36 (1987), 358-369.10.2307/2347795Suche in Google Scholar

[31] TAHIR, M. H.―CORDEIRO, G. M.―ALIZADEH, M.―MANSOOR, M.―ZUBAIR, M.―HAMEDANI, G. G.: The odd generalized exponential family of distributions with applications J. Stat. Distrib. Appl. 2 (2015), Art. No. 01.10.1186/s40488-014-0024-2Suche in Google Scholar

[32] TAHIR, M. H.―CORDEIRO, G. M.―ALIZADEH, M.―MANSOOR, M.―ZUBAIR M.: The logistic-X family of distributions and its applications Commun. Stat. Theory Methods 45 (2016), 7326-7349.10.1080/03610926.2014.980516Suche in Google Scholar

[33] TAHIR, M. H.―NADARAJAH, S.: Parameter induction in continuous univariate distributions: Well-established G families An. Acad. Bras. Ciênc.87 (2015), 539-568.10.1590/0001-3765201520140299Suche in Google Scholar PubMed

[34] TAHIR, M. H.―CORDEIRO, G. M.: Compounding of distributions: a survey and new generalized classes J. Stat. Distrib. Appl. 3 (2016), Art. No. 13.10.1186/s40488-016-0052-1Suche in Google Scholar

[35] TORABI, H.―MONTAZARI, N. H.: The gamma-uniform distribution and its application Kybernetika 48 (2012), 16-30.Suche in Google Scholar

[36] ZIMMER, W. J.―KEATS, J. B.―WANG, F. K.: The Burr XII distribution in reliability analysis J. Qual. Technol. 30 (1998), 386-394.10.1080/00224065.1998.11979874Suche in Google Scholar

[37] ZOGRAFOS, K.―BALAKRISHNAN, N.: On families of beta- and generalized gamma generated distributions and associated inference Stat. Methodol. 6 (2009), 344-362.10.1016/j.stamet.2008.12.003Suche in Google Scholar

Received: 2020-07-29
Accepted: 2020-09-02
Published Online: 2020-12-10
Published in Print: 2020-12-16

© 2020 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Regular papers
  2. Fuzzy deductive systems of RM algebras
  3. Congruence pairs of principal MS-algebras and perfect extensions
  4. The lattices of 𝔏-fuzzy state filters in state residuated lattices
  5. Central lifting property for orthomodular lattices
  6. EQ-Modules
  7. On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
  8. Remarks on some generalization of the notion of microscopic sets
  9. Disjointness of composition operators on Hv0 spaces
  10. A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
  11. The Poincaré-Cartan forms of one-dimensional variational integrals
  12. Coarse cohomology with twisted coefficients
  13. Divisible extension of probability
  14. Asymptotic behavior of the records of multivariate random sequences in a norm sense
  15. Strong convergence of the functional nonparametric relative error regression estimator under right censoring
  16. A new kumaraswamy generalized family of distributions: Properties and applications
  17. Efficient message transmission via twisted Edwards curves
  18. Computation of several Hessenberg determinants
https://doi.org/10.1515/ms-2017-0429
Schlagwörter für diesen Artikel
Burr-XII distribution; generalized family; Kumaraswamy-G family; maximum likelihood method; T-X family

Artikel in diesem Heft

  1. Regular papers
  2. Fuzzy deductive systems of RM algebras
  3. Congruence pairs of principal MS-algebras and perfect extensions
  4. The lattices of 𝔏-fuzzy state filters in state residuated lattices
  5. Central lifting property for orthomodular lattices
  6. EQ-Modules
  7. On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
  8. Remarks on some generalization of the notion of microscopic sets
  9. Disjointness of composition operators on Hv0 spaces
  10. A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
  11. The Poincaré-Cartan forms of one-dimensional variational integrals
  12. Coarse cohomology with twisted coefficients
  13. Divisible extension of probability
  14. Asymptotic behavior of the records of multivariate random sequences in a norm sense
  15. Strong convergence of the functional nonparametric relative error regression estimator under right censoring
  16. A new kumaraswamy generalized family of distributions: Properties and applications
  17. Efficient message transmission via twisted Edwards curves
  18. Computation of several Hessenberg determinants
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0429/pdf
Button zum nach oben scrollen