Home The Teissier-G family of distributions: Properties and applications
Article
Licensed
Unlicensed Requires Authentication

The Teissier-G family of distributions: Properties and applications

  • Joseph Thomas Eghwerido EMAIL logo , Lawrence Chukwudumebi Nzei , Adebola Evelyn Omotoye and Friday Ikechukwu Agu
Published/Copyright: October 16, 2022
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 72 Issue 5

Abstract

This study introduces a parsimonious and tractable generator for continuous distribution called the Teissier-G family of distributions for continuous random variables and examines the distributions belonging to this family as the sub-models. Some general statistical characteristics and sub-models of the new generator were examined and studied. Similarly, we examined the shapes of the sub-models probability density function (pdf) and hazard rate function were investigated. The parameter of the proposed model was obtained in a closed form by maximum likelihood. In addition to the numerical real life applications, Monte Carlo simulation was performed to examine the flexibility of the introduced models. The models provide good fits in all the cases. The results show great improvement compared to existing models.

Keywords: Estimation; Gompertz distribution; survival function; Teissier distribution; time series; T-X families
MSC 2010: Primary 60E05; 62E10; 62E15

  1. Communicated by Gejza Wimmer

References

[1] Afify, A. Z.—Yousof, H. M.—Cordeiro, G. M.—Ortega, E. M. M.—Nofal, Z. M.: The Weibull Fréchet distribution and its applications, J. Appl. Stat. 43(14) (2016), 2608–2626.10.1080/02664763.2016.1142945Search in Google Scholar

[2] Agu, F. I.—Eghwerido, J. T.—Runyi, F. E.: The type II Topp-Leone Generalized Power Ishita Distribution with properties and applications, Thailand Statistician 19(3) (2021), 472–483.Search in Google Scholar

[3] Agu, F. I.—Eghwerido, J. T.: Agu-Eghwerido distribution, regression model and applications, Statistics in Transition 22(4) (2021), 59–76.10.21307/stattrans-2021-038Search in Google Scholar

[4] Agu, F. I.—Paschal, I. M.—Eghwerido, J. T.: The AGU-F distribution: Properties and applications on over and underdispersed data, Int. J. Stat. Manag. Syst. 25(1) (2022), 137–155.10.1080/09720510.2020.1864940Search in Google Scholar

[5] Alizadeh, M.—Tahir, M. H.—Cordeiro, G. M.—Mansoor, M.—Zubair, M.—Hamedani, G. G.: The Kumaraswamy Marshal-Olkin family of distributions, J. Egyptian Math. Soc. 23(3) (2015), 546–557.10.1016/j.joems.2014.12.002Search in Google Scholar

[6] Alizadeh, M.—Emadi, M.—Doostparast, M.—Cordeiro, G. M.—Ortega, E. M.—Pescim, R. R.: A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications, Hacet. J. Math. Stat. 44(6) (2015), 1491–1512.10.15672/HJMS.2014418153Search in Google Scholar

[7] Alizadeh, M.—Cordeiro, G. M.—Pinho, L. G .B.—Ghosh, I.: The Gompertz-G family of distributions, J. Stat. Theory Pract. 11(1) (2017), 179–207.10.1080/15598608.2016.1267668Search in Google Scholar

[8] Alizadeh, M.—Rasekhi, M.—Yousof, H. M.—Hamedani, G. G.: The transmuted Weibull-G family of distributions Hacet. J. Math. Stat. 47(6) (2018), 1–20.10.15672/HJMS.2017.440Search in Google Scholar

[9] Alizadeh, M.—Altun, E.—Afify, A. Z.—Ozel, G.: The extended odd Weibull-G family: properties and applications, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(1) (2019), 161–186.10.31801/cfsuasmas.443699Search in Google Scholar

[10] Alizadeh, M.—Yousof, H. M.—Jahanshahi, S. M. A.—Najibi, S. M.—Hamedani, G. G.: The transmuted odd log-logistic-G family of distributions, Int. J. Stat. Manag. Syst. 23(4) (2020), 761–787.10.1080/09720510.2019.1685228Search in Google Scholar

[11] Alzaatreh, A.—Lee, C.—Famoye, F.: A new method for generating families of continuous distributions, Metron 71(1) (2013), 63–79.10.1007/s40300-013-0007-ySearch in Google Scholar

[12] Alzaghal, A.—Famoye, F.—Lee, C.: Exponentiated T-X family of distributions with some applications, International Journal of Statistics and Probability 2(3) (2013), Art. No. 31.10.5539/ijsp.v2n3p31Search in Google Scholar

[13] Amini, M.—Mirmostafaee, S. M. T. K.—Ahmadi, J.: Log-gamma generated families of distributions, Statistics 48(4) (2014), 1–20.10.1080/02331888.2012.748775Search in Google Scholar

[14] Bourguignon, B. M.—Silva, R.—Cordeiro, G. M.: The Weibull-G family of probability distributions, J. Data Sci. 12 (2014), 53–68.10.6339/JDS.201401_12(1).0004Search in Google Scholar

[15] Burr, I. W.: Cumulative frequency functions, Annals of Mathematical Statistics 13(2) (1942), 215–232.10.1214/aoms/1177731607Search in Google Scholar

[16] Cooray, K.—Ananda, M. M.: A generalization of the half-normal distribution with applications to lifetime data, Comm. Statist. Theory Methods 37(9) (2008), 1323–1337.10.1080/03610920701826088Search in Google Scholar

[17] Cordeiro, G. M.—De CASTRO, M.: A new family of generalized distributions, J. Stat. Comput. Simul 81(7) (2011), 883–898.10.1080/00949650903530745Search in Google Scholar

[18] Dey, D.—Kumar, D.—Ramos, P. L.—Louzada, F.: Exponentiated Chen distribution: properties and estimation, Comm. Statist. Simulation Comput. 46 (2017), 8118–8139.10.1080/03610918.2016.1267752Search in Google Scholar

[19] Efe-EYEFIA, E.—Eghwerido, J. T.—Zelibe, S. C.: Theoretical analysis of the Weibull alpha power inverted exponential distribution: properties and applications, Gazi Univ. J. Sci. 33(1) (2020), 265–277.10.35378/gujs.537832Search in Google Scholar

[20] Eghwerido, J. T.—Zelibe, S. C.—Ekuma-OKEREKE, E.—Efe-EYEFIA, E.: On the extented new generalized exponential distribution: properties and applications, FUPRE Journal of Scientific and Industrial Research 3(1) (2019), 112–122.Search in Google Scholar

[21] Eghwerido, J. T.—Efe-EYEFIA, E.—Zelibe, S. C.: The transmuted alpha power-G family of distributions, J. Stat. Manag. Syst. 24(5) (2021), 965–1002.10.1080/09720510.2020.1794528Search in Google Scholar

[22] Eghwerido, J. T.—David, I. J.—Adubisi, O. D.: Inverse odd Weibull generated family of distributions, Pak. J. Stat. Oper. Res 16(3) (2020), 617–633.10.18187/pjsor.v16i3.2760Search in Google Scholar

[23] Eghwerido, J. T.—Utoyo-Amrevughere, T. O.—Efe-Eyefia, E.: The alpha powerWeibull Fréchet distribution: properties and applications, Turkish Journal of Science 5(3) (2021), 170–185.Search in Google Scholar

[24] Eghwerido, J. T.—Agu, F. I.: Shifted Gompertz-G family of distributions: properties and applications, Math. Slovaca 71(5) (2021), 1291–130810.1515/ms-2021-0053Search in Google Scholar

[25] Eghwerido, J. T.—Oguntunde, P. E.—Agu, F. I.: The alpha power Marshall-Olkin-G distribution: properties, and applications, Sankhya A (2021); 10.1007/s13171-020-00235-y.Search in Google Scholar

[26] Eghwerido, J. T.—Agu, F. I.—Ibidoja, J. O.: The Shifted Exponential-G family of distributions: properties and applications, J. Stat. Manag. Syst. 25(1) (2022), 43–75.10.1080/09720510.2021.1874130Search in Google Scholar

[27] Eghwerido, J. T.—Efe-EYEFIA, E.—Otakore, O. Performance rating of the Zubair Gompertz distribution: properties and applications, J. Stat. Manag. Syst. 24(8) (2021), 1601–1626.10.1080/09720510.2020.1814500Search in Google Scholar

[28] Eghwerido, J. T.—Nzei, L. C—Agu, F. I.: Alpha power Gompertz distribution: properties and applications, Sankhya A 83(1) (2021), 449–475.10.1007/s13171-020-00198-0Search in Google Scholar

[29] Eghwerido, J. T.—Ibidoja, O. J.—Karokatose, G. B.: The exponential alpha power-G family of distributions : properties, and applications, J. Stat. Manag. Syst. 25(2) (2022), 393–422.10.1080/09720510.2021.1886734Search in Google Scholar

[30] Eliwa, M. S.—El-MORSHEDY, M.: Bivariate Gumbel-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with application, Annals of Data Science 6 (2019), 39–60.10.1007/s40745-018-00190-4Search in Google Scholar

[31] Granzotto, D. C. T.—Louzada, F. N.—Balakrishnan, N.: Cubic rank transmuted distributions: inferential issues and applications, J. Stat. Comput. Simul. 87(14) (2017), 2760–2778.10.1080/00949655.2017.1344239Search in Google Scholar

[32] Handique, L.—Chakraborty, S.—De ANDRADE, T. A. N.: The exponentiated generalized Marshall-Olkin family of distribution: its properties and applications, Annal of Data Science 6 (2019), 391–411.10.1007/s40745-018-0166-zSearch in Google Scholar

[33] Haq, M. A.—Butt, S. N.—Usman, R. M.—Fattah, A. A.: Transmuted power function distribution, Gazi Univ. J. Sci. 29(1) (2016), 177–185.Search in Google Scholar

[34] Jahanshahi, S. M. A.—Yousof, H. M.—Sharma, V. K.: The Burr X Fréchet model for extreme values: Mathematical properties, classical inference and Bayesian analysis, Pak. J. Stat. Oper. Res. 15(3) (2019), 797–818.10.18187/pjsor.v15i3.2799Search in Google Scholar

[35] Korkmaz, M. C.—Cordeiro, G. M.—Yousof, H. M.—Pescim, R. R.—Afify, A. Z.—Nadarajah, S.: The Weibull Marshall-Olkin family: Regression model and application to censored data, Comm. Statist. Theory Methods 48(16) (2019), 4171–4194.10.1080/03610926.2018.1490430Search in Google Scholar

[36] Lomax, K. S.: Business failures; Another example of the analysis of failure data, J. Amer. Statist. Assoc. 49 (1954), 847–852.10.1080/01621459.1954.10501239Search in Google Scholar

[37] Mahdavi, A.—Kundu, D.: A new method for generating distributions with an application to exponential distribution, Comm. Statist. Theory Methods 46(13) (2017), 6543–6557.10.1080/03610926.2015.1130839Search in Google Scholar

[38] Marshall, A. W.—Olkin, I.: A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), 641–652.10.1093/biomet/84.3.641Search in Google Scholar

[39] Nadarajah, S.—Cordeiro, G. M.—Ortega, E. M. M.: The exponentiated Weibull distribution: a Survey, Statistica Paper 54 (2013), 839–877.10.1007/s00362-012-0466-xSearch in Google Scholar

[40] Nadarajah, S.—Bakouch, H. S.—Tahmasbi, R.: A generalized lindley distribution, Sankhya B 73 (2011), 331–359.10.1007/s13571-011-0025-9Search in Google Scholar

[41] Nzei, L. C.—Eghwerido, J. T.—Ekhosuehi, N.: Topp-Leone Gompertz distribution: Properties and application, J. Data Sci. 18(4) (2020), 782–794.10.6339/JDS.202010_18(4).0012Search in Google Scholar

[42] Paranaiba, P. F.—Ortega,E. M.—Cordeiro, G. M.—Pascoa, M. A. D.: The Kumaraswamy Burr XII distribution: Tand practice, J. Stat. Comput. Simul. 83(11) (2013), 2117–43.10.1080/00949655.2012.683003Search in Google Scholar

[43] Ristic, M. M.—Balakrishnan, N.: The gamma-exponentiated exponential distribution, J. Stat. Comput. Simul. 82(8) (2012), 1191–1206.10.1080/00949655.2011.574633Search in Google Scholar

[44] Sharma, V. K.—Singh, S. V.—Shekhawat, K.: Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions, J. Appl. Stat. 49(2) (2022), 371–393.10.1080/02664763.2020.1813694Search in Google Scholar PubMed PubMed Central

[45] Smith, R. L.—Naylor, J. C.: A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution, Appl. Stat. 36 (1987), 258–369.10.2307/2347795Search in Google Scholar

[46] Tahir, M. H.—Cordeiro, G. M.—Alzaatreh, A.—Mansoor, M.—Zubair, M.: The logistic-X family of distributions and its applications, Comm. Statist. Theory Methods 45(24) (2016), 7326–7349.10.1080/03610926.2014.980516Search in Google Scholar

[47] Teissier, G.: Recherches sur le vieillissement et sur les lois de mortalite, Annales de Physiologie et de Physicochimie Biologique 10 (1934), 237–284.Search in Google Scholar

[48] Yousof, H. M.—Alizadeh, M.—Jahanshahi, S. M. A.—Thiago, G.—Ghosh, R. I.—Hamedani, G. G.: The transmuted Topp-Leone-G Family of distributions: Theory, characterizations and applications, J. Data Sci. 15 (2017), 723–740.10.6339/JDS.201710_15(4).00008Search in Google Scholar

[49] Yousof, H. M.—Majumder, M.—Jahanshahi, S. M. A.—Masoom, A. M.—Hamedani, G. G.: A new Weibull class of distributions: Theory, characterizations and applications, Journal of Statistical Research of Iran 15 (2018), 1–39.10.29252/jsri.15.1.45Search in Google Scholar

[50] Yousof, H. M.—Afify, A. Z.—Alizadeh, M.—Hamedani, G. G.—Jahanshahi, S. M. A.—Ghosh, I.: The generalized transmuted Poisson-G family of distributions: Theory, characterizations and applications, Pak. J. Stat. Oper. Res. 14(4) (2018), 759–779.10.18187/pjsor.v14i4.2527Search in Google Scholar

[51] Zelibe, S. C.—Eghwerido, J. T.—Efe-Eyefia, E.: Kumaraswamy alpha power inverted exponential distribution: properties and applications, Istatistik: Journal of the Turkish Statistical Association 12(1–2) (2019), 35–48.Search in Google Scholar
Received: 2021-01-28
Accepted: 2021-07-08
Published Online: 2022-10-16
Published in Print: 2022-10-26

© 2022 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular Papers
  2. Generalized hyperharmonic number sums with reciprocal binomial coefficients
  3. Gini index on generalized r-partitions
  4. Multiplicative functions of special type on Piatetski-Shapiro sequences
  5. Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
  6. Generalizations of the steffensen integral inequality for pseudo-integrals
  7. Subordination-implication problems concerning the nephroid starlikeness of analytic functions
  8. Boundedness and almost periodicity of solutions of linear differential systems
  9. On variational approaches for fractional differential equations
  10. Approximity of asymmetric metric spaces
  11. Approximation theorems for the new construction of Balázs operators and its applications
  12. On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
  13. Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
  14. Induced mappings on symmetric products of Hausdorff spaces
  15. The Teissier-G family of distributions: Properties and applications
  16. A new extension of the beta generator of distributions
  17. A new family of compound exponentiated logarithmic distributions with applications to lifetime data
  18. On two correlated linear models with common and different parameters
  19. On some applications of Duhamel operators
https://doi.org/10.1515/ms-2022-0089
Keywords for this article
Estimation; Gompertz distribution; survival function; Teissier distribution; time series; T-X families

Articles in the same Issue

  1. Regular Papers
  2. Generalized hyperharmonic number sums with reciprocal binomial coefficients
  3. Gini index on generalized r-partitions
  4. Multiplicative functions of special type on Piatetski-Shapiro sequences
  5. Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
  6. Generalizations of the steffensen integral inequality for pseudo-integrals
  7. Subordination-implication problems concerning the nephroid starlikeness of analytic functions
  8. Boundedness and almost periodicity of solutions of linear differential systems
  9. On variational approaches for fractional differential equations
  10. Approximity of asymmetric metric spaces
  11. Approximation theorems for the new construction of Balázs operators and its applications
  12. On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
  13. Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
  14. Induced mappings on symmetric products of Hausdorff spaces
  15. The Teissier-G family of distributions: Properties and applications
  16. A new extension of the beta generator of distributions
  17. A new family of compound exponentiated logarithmic distributions with applications to lifetime data
  18. On two correlated linear models with common and different parameters
  19. On some applications of Duhamel operators
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 14.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2022-0089/html
Scroll to top button