Published

2018-07-01

Form-Invariance of the Non-Regular Exponential Family of Distributions

Distribuciones de forma invariante de la familia exponencial no regular

DOI:

https://doi.org/10.15446/rce.v41n2.62233

Keywords:

Fisher information matrix, Form-invariance, Non-regular exponential family, Maximum likelihood estimation, Weighted distribution (en)
Distribución ponderada, estimación de m\'axima verosimilitud, familia exponencial no regular, invarianza de forma, matriz de información de Fisher (es)

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Authors

  • Samereh Ghorbanpour Shahid Chamran University of Ahvaz
  • Rahim Chinipardaz Shahid Chamran University of Ahvaz
  • Seyed Mohammad Reza Alavi Shahid Chamran University of Ahvaz
The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.
Las distribuciones ponderadas son usadas cuando el mecanismo de muestreo registra observaciones de acuerdo a una función no negativa. En ocasiones la forma de la función ponderada es igual a la original, excepto, posiblemente, en un cambio de parámetros y se denominan distribuciones ponderadas de forma invariante. En este artículo identificamos una clase general de funciones ponderadas e introducimos una forma extendida de distribuciones ponderadas de forma invariante, la cual incluye dos familias comunes: la familia exponencial y la familia no regular como caso particular. Algunas propiedades de estas distribuciones como las estadísticas suficientes y máximas suficientes, la estimación de máxima verosimilitud y la matriz de información de Fisher son estudiadas.

References

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S. Ghorbanpour, R. Chinipardaz & Sayed Mohammad Reza Alavi

Patil, G. & Ord, J. (1976), 'On size-biased sampling and related form-invariant weighted distributions', Sankhy a: The Indian Journal of Statistics, Series B 38(1), 48-61.

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Rao, B. (1958), 'On an analogue of cramér-rao's inequality', Scandinavian Actuarial Journal 1958(1-2), 57-67.

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How to Cite

APA

Ghorbanpour, S., Chinipardaz, R. and Alavi, S. M. R. (2018). Form-Invariance of the Non-Regular Exponential Family of Distributions. Revista Colombiana de Estadística, 41(2), 157–172. https://doi.org/10.15446/rce.v41n2.62233

ACM

[1]
Ghorbanpour, S., Chinipardaz, R. and Alavi, S.M.R. 2018. Form-Invariance of the Non-Regular Exponential Family of Distributions. Revista Colombiana de Estadística. 41, 2 (Jul. 2018), 157–172. DOI:https://doi.org/10.15446/rce.v41n2.62233.

ACS

(1)
Ghorbanpour, S.; Chinipardaz, R.; Alavi, S. M. R. Form-Invariance of the Non-Regular Exponential Family of Distributions. Rev. colomb. estad. 2018, 41, 157-172.

ABNT

GHORBANPOUR, S.; CHINIPARDAZ, R.; ALAVI, S. M. R. Form-Invariance of the Non-Regular Exponential Family of Distributions. Revista Colombiana de Estadística, [S. l.], v. 41, n. 2, p. 157–172, 2018. DOI: 10.15446/rce.v41n2.62233. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/62233. Acesso em: 28 mar. 2025.

Chicago

Ghorbanpour, Samereh, Rahim Chinipardaz, and Seyed Mohammad Reza Alavi. 2018. “Form-Invariance of the Non-Regular Exponential Family of Distributions”. Revista Colombiana De Estadística 41 (2):157-72. https://doi.org/10.15446/rce.v41n2.62233.

Harvard

Ghorbanpour, S., Chinipardaz, R. and Alavi, S. M. R. (2018) “Form-Invariance of the Non-Regular Exponential Family of Distributions”, Revista Colombiana de Estadística, 41(2), pp. 157–172. doi: 10.15446/rce.v41n2.62233.

IEEE

[1]
S. Ghorbanpour, R. Chinipardaz, and S. M. R. Alavi, “Form-Invariance of the Non-Regular Exponential Family of Distributions”, Rev. colomb. estad., vol. 41, no. 2, pp. 157–172, Jul. 2018.

MLA

Ghorbanpour, S., R. Chinipardaz, and S. M. R. Alavi. “Form-Invariance of the Non-Regular Exponential Family of Distributions”. Revista Colombiana de Estadística, vol. 41, no. 2, July 2018, pp. 157-72, doi:10.15446/rce.v41n2.62233.

Turabian

Ghorbanpour, Samereh, Rahim Chinipardaz, and Seyed Mohammad Reza Alavi. “Form-Invariance of the Non-Regular Exponential Family of Distributions”. Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 157–172. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/62233.

Vancouver

1.
Ghorbanpour S, Chinipardaz R, Alavi SMR. Form-Invariance of the Non-Regular Exponential Family of Distributions. Rev. colomb. estad. [Internet]. 2018 Jul. 1 [cited 2025 Mar. 28];41(2):157-72. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/62233

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