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

The shifted Gompertz-G family of distributions: Properties and applications

  • Joseph Thomas Eghwerido EMAIL logo and Friday Ikechukwu Agu
Published/Copyright: October 4, 2021
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 5

Abstract

This article proposes a class of generator for classical statistical distribution called the shifted Gompertz-G (SHIGO-G) distribution for generating new continuous distributions. Special models of the proposed model were examined together with some of its statistical properties in closed form which makes it tractable for censored data. Its major properties include heavy tail, approximately symmetric, left and right skewed with a combination of exponential and a reverted Gumbel distributions called the Gompertz. The bivariate SHIGO-G is introduced. The parameters estimate of the proposed model was obtained by maximum likelihood method. A Monte Carlo simulation study was employed to investigate the performance of the estimators of the proposed model mean, variance, bias and mean square error. A two real life illustration was used to examine the empirical goodness-of-fit of the test statistic of the proposed model. The results of the real life applications show that the SHIGO-G model provides a better fit for the data set used.

Keywords: Bivariate shifted Gompertz; exponential distribution; Gumbel distribution; maximum likelihood; shifted Gompertz distribution
MSC 2010: Primary 60E05; 62E10; Secondary 62E15

  1. (Communicated by Gejza Wimmer)

References

[1] Afify, A. Z.—Yousof, H. M.—Nadarajah, S.: The beta transmuted-H family of distributions: properties and applications, Stat. Interface 10 (2016), 505–520.10.4310/SII.2017.v10.n3.a13Search in Google Scholar

[2] 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

[3] 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

[4] 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

[5] Alizadeh, M.—Yousof, H. M.—Jahanshahi, S. M. A.—Najibi, S. M.—Hamedani, G. G.: The transmuted odd log-logistic-G family of distributions, Journal of Statistics and Management Systems 23 (2020), 761–787.10.1080/09720510.2019.1685228Search in Google Scholar

[6] 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

[7] 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

[8] Aljarrah, M. A.—Lee, C.—F. Famoye, F.: On generating T-X family of distributions using quantile functions, Journal of Statistical Distributions and Applications 1(1) (2014), 1–17.10.1186/2195-5832-1-2Search in Google Scholar

[9] 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

[10] Aryal, G. R.—Yousof, H. M.: The exponentiated generalized-g Poisson family of distributions, Economic Quality Control 32(1) (2017), 1–17.10.1515/eqc-2017-0004Search in Google Scholar

[11] Bemmaor, A. C.: Modelling the diffusion of new durable goods: Word of mouth effect versus consumer heterogeneity. In: Research Traditions in Marketing (G. Laurent, G. L. Lilien and B. Pras, eds.), Boston, Kluwer Academic Publishers, 1994, pp. 201–223.10.1007/978-94-011-1402-8_6Search in Google Scholar

[12] 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

[13] Braga, S. A.—Cordeiro, G. M.—Ortega, E. M.—Nilton da Cruz, J.: The odd log-logistic normal distribution: Theory and applications in analysis of experiments, J. Stat. Theory Pract. 10(2) (2016), 311–335.10.1080/15598608.2016.1141127Search in Google Scholar

[14] 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

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

[16] Eghwerido, J. T.—Oguntunde, P. E.—Agu, F. I.: The alpha power Marshall-Olkin-G distribution: Properties, and applications, Sankhya A (2020), https://doi.org/10.1007/s13171-020-00235-y.10.1007/s13171-020-00235-ySearch in Google Scholar

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

[18] Eghwerido, J. T.—Ikwuoche, D. J.—Adubisi, D. O.: 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

[19] Eghwerido, J. T.—Zelibe, S. C.—Ekuma-Okereke, E.—Efe-Eyefia, E.: On the extented new generalized exponential distribution: properties and applications, FUPRE J. Sci. Ind. Res. 3(1) (2019), 112–122.Search in Google Scholar

[20] Eghwerido, J. T.—Zelibe, S. C.—Efe-Eyefia, E.: Gompertz-alpha power inverted exponential distribution: properties and applications, Thailand Statistician 18(3) (2020), 319–332.Search in Google Scholar

[21] Eghwerido, J. T.—Efe-Eyefia, E.—Otakore, O.: Performance rating of the Zubair Gompertz distribution: properties and applications, J. Stat. Manag. Syst. (2021); https://doi.org/10.1080/09720510.2020.1814500.10.1080/09720510.2020.1814500Search in Google Scholar

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

[23] 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

[24] Jiménez, F.—Jodrá, P.: A note on the moments and computer generation of the shifted Gompertz distribution, Comm. Statist. Theory Methods 38(1) (2009), 75–89.10.1080/03610920802155502Search in Google Scholar

[25] Jiménez, F.: Estimation of parameters of the shifted Gompertz distribution using least squares, maximum likelihood and moments methods, J. Comput. Appl. Math. 255 (2014), 867–877.10.1016/j.cam.2013.07.004Search in Google Scholar

[26] Jodrá, P.: A bounded distribution derived from the shifted Gompertz law, Journal of King Saud University of Science (2018), https://doi.org/10.1016/j.jksus.2018.08.001.10.1016/j.jksus.2018.08.001Search in Google Scholar

[27] Khaleel, M. A.—Oguntunde, P. E.—Ahmed, M. T.—Ibrahim, N. A.—Loh, Y. F.: The Gompertz flexible Weibull distribution and its applications, Malays. J. Math. Sci. 14(1) (2020), 169–190.Search in Google Scholar

[28] 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

[29] Navarro, J.—Franco, M.—Ruiz, J. M.: Characterization through moments of the residual life and conditional spacing, Sankya: Ind. J. Stat. 60(1) (1998), 36–48.Search in Google Scholar

[30] 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

[31] Reyad, H.—Alizadeh, M.—Jamal, F.—Othman, S.: The Topp Leone odd Lindley-G family of distributions : Properties and applications, J. Stat. Manag. Syst. 21(7) (2018), 1273–1297.10.1080/09720510.2018.1495157Search in Google Scholar

[32] Sindhu, T. N.—Aslam, M.—Hussain, Z.: A simulation study of parameters for the censored shifted Gompertz mixture distribution: A Bayesian approach, J. Stat. Manag. Syst. 19(3) (2016), 423–450.10.1080/09720510.2015.1103462Search in Google Scholar

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

[34] 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), 7326–7348.10.1080/03610926.2014.980516Search in Google Scholar

[35] Turnbull, B. C.—Ghosh, S. K: Unimodal density estimation using Bernstein polynomials, Comput. Statist. Data Anal. 72 (2013), 13–29.10.1016/j.csda.2013.10.021Search in Google Scholar

[36] Yousof, H. M.—Afify, A. Z.—Alizadeh, M.—Nadarajah, S.—Aryal, G. R.—Hamedani, G. G.: The Marshall-Olkin generalized-G family of distributions with applications, Statistica 78(3) (2018), 273–295.Search in Google Scholar

[37] Yousof, H. M.—Alizadeh, M.—Jahanshahi, S. M. A.—Ramires, T. G.—Ghosh, I.—Hamedani, G. G.: The transmuted Topp-Leone-G family of distributions: theory, characterizations and applications, J. Data Sci. 15 (2017), 672-740.10.6339/JDS.201710_15(4).00008Search in Google Scholar

[38] Yousof, H. M.—Afify, A. Z.—Hamedani, G. G.—Aryal, G.: The Burr-X generator of distributions for lifetime data, J. Stat. Theory Appl. 16 (2017), 288–305.10.2991/jsta.2017.16.3.2Search in Google Scholar

[39] 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, J. Statist. Res. of Iran 15 (2018), 1–39.10.29252/jsri.15.1.1Search in Google Scholar

[40] 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

[41] Zelibe, S. C.—Eghwerido, J. T.—Efe-Eyefia, E.: Kumaraswamy alpha power inverted exponential distribution: properties and applications, Istatistik 12(1) (2019), 35–48.Search in Google Scholar
Received: 2020-08-06
Accepted: 2020-10-30
Published Online: 2021-10-04
Published in Print: 2021-10-26

© 2021 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem
  3. Polynomial functions on rings of dual numbers over residue class rings of the integers
  4. Sufficient conditions for p-valent functions
  5. Upper bounds for analytic summand functions and related inequalities
  6. Global structure for a fourth-order boundary value problem with sign-changing weight
  7. On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE
  8. Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
  9. Properties of critical and subcritical second order self-adjoint linear equations
  10. Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
  11. Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
  12. Poisson like matrix operator and its application in p-summable space
  13. On the homological and algebraical properties of some Feichtinger algebras
  14. Disjoint topological transitivity for weighted translations generated by group actions
  15. On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations
  16. Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
  17. The shifted Gompertz-G family of distributions: Properties and applications
  18. On the testing hypothesis in uniform family of distributions with nuisance parameter
  19. Clarkson inequalities related to convex and concave functions
https://doi.org/10.1515/ms-2021-0053
Keywords for this article
Bivariate shifted Gompertz; exponential distribution; Gumbel distribution; maximum likelihood; shifted Gompertz distribution

Articles in the same Issue

  1. Regular papers
  2. Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem
  3. Polynomial functions on rings of dual numbers over residue class rings of the integers
  4. Sufficient conditions for p-valent functions
  5. Upper bounds for analytic summand functions and related inequalities
  6. Global structure for a fourth-order boundary value problem with sign-changing weight
  7. On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE
  8. Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
  9. Properties of critical and subcritical second order self-adjoint linear equations
  10. Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
  11. Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
  12. Poisson like matrix operator and its application in p-summable space
  13. On the homological and algebraical properties of some Feichtinger algebras
  14. Disjoint topological transitivity for weighted translations generated by group actions
  15. On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations
  16. Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
  17. The shifted Gompertz-G family of distributions: Properties and applications
  18. On the testing hypothesis in uniform family of distributions with nuisance parameter
  19. Clarkson inequalities related to convex and concave functions
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 15.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2021-0053/html
Scroll to top button