Moments and Estimation of the Exponentiated Moment Exponential Distribution

Devendra Kumar

doi:10.36753/mathenot.421415

EN

Moments and Estimation of the Exponentiated Moment Exponential Distribution

Abstract

A new extension of moment exponential distribution, called exponentiated moment exponential distribution (EMED), was recently introduced by Hasnain [14]. Based on lower generalized order statistics, we first derive the explicit expressions as well as recurrence relations for single and product moments of lower generalized order statistics and we use these results to compute the means, variances and coefficients of skewness and kurtosis of EMED. Further, using a recurrence relation for single moment, we obtain characterization of EMED. Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED. Finally, we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters. We have are also derived the Bayes interval of this distribution. Monte Carlo simulations are performed to compare the performances of the proposed methods.

Keywords

explicit expression,Recurrence relation,Lower generalized order statistics,Order statistics,Record values,Exponentiated moment exponential distribution,Bayes estimator,General entropy loss function,Maximum likelihood estimator

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Devendra Kumar

Publication Date

April 15, 2016

Submission Date

March 4, 2015

Acceptance Date

-

Published in Issue

Year 2016 Volume: 4 Number: 1

DOI

https://doi.org/10.36753/mathenot.421415

IZ

https://izlik.org/JA32YY47DS

APA

Kumar, D. (2016). Moments and Estimation of the Exponentiated Moment Exponential Distribution. Mathematical Sciences and Applications E-Notes, 4(1), 94-112. https://doi.org/10.36753/mathenot.421415

AMA

1.Kumar D. Moments and Estimation of the Exponentiated Moment Exponential Distribution. Math. Sci. Appl. E-Notes. 2016;4(1):94-112. doi:10.36753/mathenot.421415

Chicago

Kumar, Devendra. 2016. “Moments and Estimation of the Exponentiated Moment Exponential Distribution”. Mathematical Sciences and Applications E-Notes 4 (1): 94-112. https://doi.org/10.36753/mathenot.421415.

EndNote

Kumar D (April 1, 2016) Moments and Estimation of the Exponentiated Moment Exponential Distribution. Mathematical Sciences and Applications E-Notes 4 1 94–112.

IEEE

[1]D. Kumar, “Moments and Estimation of the Exponentiated Moment Exponential Distribution”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 94–112, Apr. 2016, doi: 10.36753/mathenot.421415.

ISNAD

Kumar, Devendra. “Moments and Estimation of the Exponentiated Moment Exponential Distribution”. Mathematical Sciences and Applications E-Notes 4/1 (April 1, 2016): 94-112. https://doi.org/10.36753/mathenot.421415.

JAMA

1.Kumar D. Moments and Estimation of the Exponentiated Moment Exponential Distribution. Math. Sci. Appl. E-Notes. 2016;4:94–112.

MLA

Kumar, Devendra. “Moments and Estimation of the Exponentiated Moment Exponential Distribution”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, Apr. 2016, pp. 94-112, doi:10.36753/mathenot.421415.

Vancouver

1.Devendra Kumar. Moments and Estimation of the Exponentiated Moment Exponential Distribution. Math. Sci. Appl. E-Notes. 2016 Apr. 1;4(1):94-112. doi:10.36753/mathenot.421415