[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

The unit Muth distribution: statistical properties and applications

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper introduces a bounded probability distribution which is derived from the Muth distribution. The main statistical properties are studied and analytical expressions are provided for the moments, incomplete moments, inverse of the cumulative distribution function, extropy, Lorentz and Bonferroni curves, among others. Moreover, it possesses both monotone and non-monotone hazard rate functions so the new distribution is rich enough to model real data. Different estimation methods are applied to estimate the parameters of the model and a Monte Carlo simulation study assesses their performances. The usefulness in practical applications is illustrated using two real data sets and the results show that the proposed distribution provides better fits than other competing distributions commonly used to model data with bounded support.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Abd EL-Baset, A. A., Ghazal, M. G. M.: Exponentiated additive Weibull distribution. Reliab. Eng. Syst. Saf. 193, 106663 (2020)

  2. Babu, G.J., Rao, C.R.: Goodness-of-fit tests when parameters are estimated. Sankhya 66(1), 63–74 (2004)

    MathSciNet  Google Scholar 

  3. Bakouch, H. S., Nik, A. S., Asgharzadeh, A., Salinas, H. S.: A flexible probability model for proportion data: Unit-half-normal distribution. Commun. Stat. Case. Stud. Data. Anal. Appl. 1–18 (2021)

  4. Bebbington, M., Lai, C.D., Murthy, D.N.P., Zitikis, R.: Modelling N- and W-shaped hazard rate functions without mixing distributions. Proc. Inst. Mech. Eng. O. J. Risk. Reliab. 223(1), 59–69 (2009)

    Google Scholar 

  5. Caramanis, M., Stremel, J., Fleck, W., Daniel, S.: Probabilistic production costing: An investigation of alternative algorithms. Int. J. Electr. Power. Energy. Syst. 5(2), 75–86 (1983)

    Article  Google Scholar 

  6. Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert \(W\) function. Adv. Comput. Math. 5(1), 329–359 (1996)

    Article  MathSciNet  Google Scholar 

  7. D’Agostino, R.B., Stephens, M.A.: Goodness-Fit Tech. Marcel Dekker, New York (1986)

  8. Ghitany, M.E., Mazucheli, J., Menezes, A.F.B., Alqallaf, F.: The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Commun. Stat. Theory. Methods. 48(14), 3423–3438 (2019)

    Article  MathSciNet  Google Scholar 

  9. Gómez-Déniz, E., Sordo, M.A., Calderín-Ojeda, E.: The Log-Lindley distribution as an alternative to the beta regression model with applications in insurance. Insur. Math. Econ. 54, 49–57 (2014)

    Article  MathSciNet  Google Scholar 

  10. Haq, M. A. U., Hashmi, S., Aidi, K., Ramos, P. L., Louzada, F.: Unit modified Burr-III distribution: Estimation, characterizations and validation test. Ann. Data. Sci. 1–26 (2020)

  11. Irshad, M.R., Maya, R., Arun, S.P.: Muth distribution and estimation of a parameter using order statistics. Statistica 81(1), 93–119 (2021)

    Google Scholar 

  12. Irshad, M.R., Maya, R., Krishna, A.: Exponentiated power muth distribution and associated inference. J. Indian. Soc. Probab. Stat. 22(2), 265–302 (2021)

    Article  Google Scholar 

  13. Irshad, M.R., Shibu, D.S., Maya, R., D’cruz, V.: Binominal mixture lindley distribution: properties and applications. J. Indian. Soc. Probab. Stat. 21(2), 437–469 (2020)

  14. Jodrá, P.: A bounded distribution derived from the shifted Gompertz law. J. King. Saud. Univ. Sci. 32, 523–536 (2020)

    Article  Google Scholar 

  15. Jodrá, P., Gómez, H.W., Jiménez-Gamero, M.D., Alba-Fernández, M.V.: The power Muth distribution. Math. Model. Anal. 22(2), 186–201 (2017)

    Article  MathSciNet  Google Scholar 

  16. Jodrá, P., Jiménez-Gamero, M.D.: A note on the log-lindley distribution. Insur. Math. Econ. 71, 186–194 (2016)

    Article  MathSciNet  Google Scholar 

  17. Jodrá, P., Jiménez-Gamero, M.D.: A quantile regression model for bounded responses based on the exponential-geometric distribution. Revstat. Stat. J. 18(4), 415–436 (2020)

    MathSciNet  Google Scholar 

  18. Jodrá, P., Jiménez-Gamero, M.D., Alba-Fernández, M.V.: On the muth distribution. Math. Model. Anal. 20(3), 291–310 (2015)

    Article  MathSciNet  Google Scholar 

  19. Khalil, A., Ijaz, M., Ali, K., Mashwani, W.K., Shafiq, M., Kumam, P., Kumam, W.: A novel flexible additive Weibull distribution with real-life applications. Commun. Stat. Theory. Methods. 50(7), 1557–1572 (2021)

    Article  MathSciNet  Google Scholar 

  20. Korkmaz, M.Ç.: A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application. J. Appl. Stat. 47(12), 2097–2119 (2020)

    Article  MathSciNet  Google Scholar 

  21. Kumaraswamy, P.: A generalized probability density function for double-bounded random processes. J. Hydrol. 46(1), 79–88 (1980)

    Article  Google Scholar 

  22. Leemis, L.M., McQueston, J.T.: Univariate distribution relationships. Am. Stat. 62(1), 45–53 (2008)

    Article  MathSciNet  Google Scholar 

  23. Lehmann, E.L., Casella, G.: Theory of Point Estimation, 2nd edn. Springer Texts in Statistics. Springer-Verlag, New York (1998)

    Google Scholar 

  24. Mazucheli, J., Menezes, A.F.B., Chakraborty, S.: On the one parameter unit-Lindley distribution and its associated regression model for proportion data. J. Appl. Stat. 46(4), 700–714 (2019)

    Article  MathSciNet  Google Scholar 

  25. Mazucheli, J., Menezes, A.F., Dey, S.: Unit-Gompertz distribution with applications. Statistica 79(1), 25–43 (2019)

    Google Scholar 

  26. Mazucheli, J., Menezes, A.F.B., Fernandes, L.B., de Oliveira, R.P., Ghitany, M.E.: The unit-Weibull distribution as an alternative to the kumaraswamy distribution for the modeling of quantiles conditional on covariates. J. Appl. Stat. 47(6), 954–974 (2020)

    Article  MathSciNet  Google Scholar 

  27. Mazumdar, M., Gaver, D.P.: On the computation of power-generating system reliability indexes. Technometrics 26(2), 173–185 (1984)

    Article  Google Scholar 

  28. Modi, K., Gill, V.: Unit Burr-III distribution with application. J. Stat. Manag. Syst. 23(3), 579–592 (2020)

    Google Scholar 

  29. Muth, E.J.: Reliability models with positive memory derived from the mean residual life function. Theory. Appl. Reliab. 2, 401–435 (1977)

    Google Scholar 

  30. Pourdarvish, A., Mirmostafaee, S.M.T.K., Naderi, K.: The exponentiated Topp-Leone distribution: properties and application. J. Appl. Environ. Biol. Sci. 5(7S), 251–256 (2015)

    Google Scholar 

  31. R Development Core Team, 2021. R: A language and environment for statistical computing. R Found Stat Comput, Vienna, Austria. URL http://www.R-project.org/

  32. Rinne, H.: Estimating the lifetime distribution of private motor-cars using prices of used cars: The Teissier model. Stat. Zwischen. Theor. Prax. 172–184 (1981)

  33. Suprawhardana, M.S., Prayoto, S.: Total time on test plot analysis for mechanical components of the RSG-GAS reactor. At. Indones. 25(2), 81–90 (1999)

    Google Scholar 

  34. Swain, J.J., Venkatraman, S., Wilson, J.R.: Least-squares estimation of distribution functions in Johnson’s translation system. J. Stat. Comput. Simul. 29(4), 271–297 (1988)

    Article  Google Scholar 

  35. Teissier, G.: Recherches sur le vieillissement et sur les lois de la mortalité. Annal de physiol et de physicochimie biologique 10(2), 237–284 (1934)

    Google Scholar 

  36. Topp, C.W., Leone, F.C.: A family of J-shaped frequency functions. J. Am. Stat. Assoc. 50(269), 209–219 (1955)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Research of Pedro Jodrá has been partially funded by Diputación General de Aragón –Grupo E24-17R– and ERDF funds.

Author information

Authors and Affiliations

  1. Department of Statistics, Goverment College for Women, Trivandrum, Kerala, 695 014, India

    R. Maya

  2. Departamento de Métodos Estadísticos, EINA, Universidad de Zaragoza, 50018, Zaragoza, Spain

    P. Jodrá

  3. Department of Statistics, Cochin University of Science and Technology, Cochin, Kerala, 682 022, India

    M. R. Irshad & A. Krishna

Authors
  1. R. Maya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Jodrá
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. R. Irshad
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Krishna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. R. Irshad.

Ethics declarations

Conflicts of interest

The corresponding author states that there is no conflict of interest on behalf of all the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maya, R., Jodrá, P., Irshad, M.R. et al. The unit Muth distribution: statistical properties and applications. Ricerche mat 73, 1843–1866 (2024). https://doi.org/10.1007/s11587-022-00703-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-022-00703-7

Keywords

Mathematics Subject Classification