Published

2014-01-01

A New Extension of the Exponential Distribution

Una nueva extensión de la distribución exponencial

DOI:

https://doi.org/10.15446/rce.v37n1.44355

Keywords:

Exponential distribution, Mixtures of distribution, Likelihood (en)
distribución exponencial, mezcla de distribuciones, verosimilitud (es)

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Authors

  • Yolanda M. Gómez Universidade de São Paulo
  • Heleno Bolfarine Universidade de São Paulo
  • Héctor W. Gómez Universidad de Antofagasta

The present paper considers an extension of the exponential distribution based on mixtures of positive distributions. We study the main properties of this new distribution, with special emphasis on its moments, moment generator function and some characteristics related to reliability studies. We also discuss parameter estimation considering the maximum likelihood and moments approach. An application reveals that the model proposed can be very useful in fitting real data. A final discussion concludes the paper.

En el presente paper se considera una extensión de la distribución exponencial basada en mezclas de distribuciones positivas. Estudiamos las principales propiedades de esta nueva distribución, con especial énfasis en sus momentos, función generadora de momentos, y algunas características relacionadas a estudios de confiabilidad. También se analiza la estimación de parámetros a través de los métodos de momentos y de máxima verosimilitud. Una aplicación muestra que el modelo propuesto puede ser muy útil para ajustar datos reales. Una discusión final concluye el artículo.

https://doi.org/10.15446/rce.v37n1.44355

A New Extension of the Exponential Distribution

Una nueva extensión de la distribución exponencial

YOLANDA M. GÓMEZ1, HELENO BOLFARINE2, HÉCTOR W. GÓMEZ3

1Universidade de São Paulo, Instituto de Matematica e Estatística, São Paulo, Brazil. Professor. Email: ymgomez@ime.usp.br
2Universidade de São Paulo, Instituto de Matematica e Estatística, São Paulo, Brazil. Professor. Email: hbolfar@ime.usp.br
3Universidad de Antofagasta, Facultad de Ciencias Básicas, Departamento de Matemáticas, Antofagasta, Chile. Professor. Email: hector.gomez@uantof.cl

Abstract

The present paper considers an extension of the exponential distribution based on mixtures of positive distributions. We study the main properties of this new distribution, with special emphasis on its moments, moment generator function and some characteristics related to reliability studies. We also discuss parameter estimation considering the maximum likelihood and moments approach. An application reveals that the model proposed can be very useful in fitting real data. A final discussion concludes the paper.

Key words: Exponential distribution, Mixtures of distribution, Likelihood.

Resumen

En el presente paper se considera una extensión de la distribución exponencial basada en mezclas de distribuciones positivas. Estudiamos las principales propiedades de esta nueva distribución, con especial énfasis en sus momentos, función generadora de momentos, y algunas características relacionadas a estudios de confiabilidad. También se analiza la estimación de parámetros a través de los métodos de momentos y de máxima verosimilitud. Una aplicación muestra que el modelo propuesto puede ser muy útil para ajustar datos reales. Una discusión final concluye el artículo.

Palabras clave: distribución exponencial, mezcla de distribuciones, verosimilitud.

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References

1. Akaike, H. (1974), 'A new look at statistical model identification', IEEE Transaction on Automatic Control AC-19(6), 716-723.

2. Andrews, D. F. & Herzberg, A. M. (1985), Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.

3. Barlow, R. E., Toland, R. H. & Freeman, T. (1984), A Bayesian analysis of stress-rupture life of kevlar 49/epoxy spherical pressure vessels, 'Proc. Conference on Applications of Statistics', Marcel Dekker, New York.

4. Gupta, R. D. & Kundu, D. (1999), 'Generalized exponential distributions', Australian and New Zealand Journal of Statistics 41(2), 173-188.

5. Gupta, R. D. & Kundu, D. (2001), 'Exponentiated exponential family: An alternative to Gamma and Weibull distribution', Biometrical Journal 43(1), 117-130.

6. Marshall, A. W. & Olkin, I. (2007), Life Distributions: Structure of Nonparametric, Semiparametric and Parametric Families, Springer Series in Statistics.

7. Nadarajah, S. & Haghighi, F. (2011), 'An extension of the exponential distribution', Statistics: A Journal of Theoretical and Applied Statistics 45(6), 543-558.

[Recibido en enero de 2013. Aceptado en diciembre de 2013]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n1a02,
    AUTHOR  = {Gómez, Yolanda M. and Bolfarine, Heleno and Gómez, Héctor W.},
    TITLE   = {{A New Extension of the Exponential Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {1},
    pages   = {25-34}
}

References

Akaike, H. (1974), ‘A new look at statistical model identification’, IEEE Transaction on Automatic Control AC-19(6), 716–723.

Andrews, D. F. & Herzberg, A. M. (1985), Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.

Barlow, R. E., Toland, R. H. & Freeman, T. (1984), A Bayesian analysis of stressrupture life of kevlar 49/epoxy spherical pressure vessels, in ‘Proc. Conference on Applications of Statistics’, Marcel Dekker, New York.

Gupta, R. D. & Kundu, D. (1999), ‘Generalized exponential distributions’, Australian and New Zealand Journal of Statistics 41(2), 173–188.

Gupta, R. D. & Kundu, D. (2001), ‘Exponentiated exponential family: An alternative to Gamma and Weibull distribution’, Biometrical Journal 43(1), 117–130.

Marshall, A. W. & Olkin, I. (2007), Life Distributions: Structure of Nonparametric, Semiparametric and Parametric Families.

Nadarajah, S. & Haghighi, F. (2011), ‘An extension of the exponential distribution’, Statistics: A Journal of Theoretical and Applied Statistics 45(6), 543– 558.

How to Cite

APA

Gómez, Y. M., Bolfarine, H. and Gómez, H. W. (2014). A New Extension of the Exponential Distribution. Revista Colombiana de Estadística, 37(1), 25–34. https://doi.org/10.15446/rce.v37n1.44355

ACM

[1]
Gómez, Y.M., Bolfarine, H. and Gómez, H.W. 2014. A New Extension of the Exponential Distribution. Revista Colombiana de Estadística. 37, 1 (Jan. 2014), 25–34. DOI:https://doi.org/10.15446/rce.v37n1.44355.

ACS

(1)
Gómez, Y. M.; Bolfarine, H.; Gómez, H. W. A New Extension of the Exponential Distribution. Rev. colomb. estad. 2014, 37, 25-34.

ABNT

GÓMEZ, Y. M.; BOLFARINE, H.; GÓMEZ, H. W. A New Extension of the Exponential Distribution. Revista Colombiana de Estadística, [S. l.], v. 37, n. 1, p. 25–34, 2014. DOI: 10.15446/rce.v37n1.44355. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/44355. Acesso em: 28 mar. 2025.

Chicago

Gómez, Yolanda M., Heleno Bolfarine, and Héctor W. Gómez. 2014. “A New Extension of the Exponential Distribution”. Revista Colombiana De Estadística 37 (1):25-34. https://doi.org/10.15446/rce.v37n1.44355.

Harvard

Gómez, Y. M., Bolfarine, H. and Gómez, H. W. (2014) “A New Extension of the Exponential Distribution”, Revista Colombiana de Estadística, 37(1), pp. 25–34. doi: 10.15446/rce.v37n1.44355.

IEEE

[1]
Y. M. Gómez, H. Bolfarine, and H. W. Gómez, “A New Extension of the Exponential Distribution”, Rev. colomb. estad., vol. 37, no. 1, pp. 25–34, Jan. 2014.

MLA

Gómez, Y. M., H. Bolfarine, and H. W. Gómez. “A New Extension of the Exponential Distribution”. Revista Colombiana de Estadística, vol. 37, no. 1, Jan. 2014, pp. 25-34, doi:10.15446/rce.v37n1.44355.

Turabian

Gómez, Yolanda M., Heleno Bolfarine, and Héctor W. Gómez. “A New Extension of the Exponential Distribution”. Revista Colombiana de Estadística 37, no. 1 (January 1, 2014): 25–34. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/44355.

Vancouver

1.
Gómez YM, Bolfarine H, Gómez HW. A New Extension of the Exponential Distribution. Rev. colomb. estad. [Internet]. 2014 Jan. 1 [cited 2025 Mar. 28];37(1):25-34. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/44355

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