Browse > Article
http://dx.doi.org/10.7465/jkdi.2017.28.5.1205

Estimation based on lower record values from exponentiated Pareto distribution  

Yoon, Sanggyeong (Department of Statistics, Pusan National University)
Cho, Youngseuk (Department of Statistics, Pusan National University)
Lee, Kyeongjun (Department of Computer Science and Statistics, Daegu University, Daegu University & Institute of Basic Science, Deagu University)
Publication Information
Journal of the Korean Data and Information Science Society / v.28, no.5, 2017 , pp. 1205-1215 More about this Journal
Abstract
In this paper, we aim to estimate two scale-parameters of exponentiated Pareto distribution (EPD) based on lower record values. Record values arise naturally in many real life applications involving data relating to weather, sport, economics and life testing studies. We calculate the Bayesian estimators for the two parameters of EPD based on lower record values. The Bayes estimators of two parameters for the EPD with lower record values under the squared error loss (SEL), linex loss (LL) and entropy loss (EL) functions are provided. Lindley's approximate method is used to compute these estimators. We compare the Bayesian estimators in the sense of the bias and root mean squared estimates (RMSE).
Keywords
Bayesian estimation; balanced loss function; exponentiated Pareto distribution; Lindley's approximation; lower record values;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Abd-El-Hakim, N. S. and Sultan, K. S. (2001). Maximum likelihood estimates of Weibull parameters based on record values. Journal of the Egyptian Mathematical Society, 9, 79-89.
2 Ahmadi, J., Jozani, M., Marchand, E. and Parsian, A. (2009). Bayes estimation based on k-record data from a general class of distributions under balanced type loss functions. Journal of Statistical Planning and Inference, 139, 1180-1189.   DOI
3 Arnold, B. C. and Press, S. J. (1983). Bayesian inference for Pareto populations. Journal of Econometrics, 21, 287-306.   DOI
4 Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Records, John Wiley, New York.
5 Balakrishnan, N. and Chan, P. S. (1993). Record values from Rayleigh and Weibull distributions and associated inference. National Institute of Standards and Technology Journal of Research, 866, 41-51.
6 Bourguignon, M., Silva, R. B., Zea, L. M. and Cordeiro, G. M. (2013). The Kumaraswamy Pareto distribution. Journal of Statistical Theory and Applications, 12, 129-144.   DOI
7 Calabria, R. and Pulcini, G. (1996). Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics-Theory and Methods, 25, 585-600.   DOI
8 Chandler, K. N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society Series B (Methodological), 220-228.
9 Choulakian, V. and Stephens, M. A. (2001). Goodness-of-fit tests for the generalized Pareto distribution. Technometrics, 43, 478-484.   DOI
10 Gupta, R. C., Gupta, R. D. and Gupta, P. L. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory Methods, 27, 887-904.   DOI
11 Gupta, R. D. and Kundu D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41, 173-188.   DOI
12 Gupta, R. D. and Kundu, D. (2001a). Generalized exponential distribution: Different method of estimations. Journal of Statistical Computation and Simulation, 69, 315-337.   DOI
13 Gupta, R. D. and Kundu, D. (2001b). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal, 1, 117-130.
14 Gupta, R. D. and Kundu D. (2006). On the comparison of Fisher information of the Weibull and GE distributions. Journal of Statistical Planning and Inference, 136, 3130-3144.   DOI
15 Jozani, M., Marchand, E. and Parsian, A. (2012). Bayes and robust Bayesian estimation under a general class of balanced loss functions. Statistical Paper, 53, 51-60.   DOI
16 Kim, C., Jung, J. and Chung, Y. (2011). Bayesian estimation for the exponentiated Weibull model under type II progressive censoring. Statistical Papers, 52, 53-70.   DOI
17 Lee, K. (2017). Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data. Journal of the Korean Data & Information Science Society, 28, 659-668.
18 Lee, K. and Cho, Y. (2015). Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data. Journal of the Korean Data & Information Science Society, 26, 1573-1582.   DOI
19 Mudholkar, G. S. and Hutson, A. D. (1996). The exponentiated Weibull family: Some properties and a flood data application. Communications in Statistics-Theory Methods, 25, 3059-3083.   DOI
20 Nadarajah, S. (2005). Exponentiated Pareto distributions. Statistics, 39, 255-260.   DOI
21 Nassar, M. M. and Eissa, F. H. (2003). On the exponentiated Weibull distribution. Communications in Statistics-Theory and Methods, 32, 1317-1336.   DOI
22 Raqab, M. Z. (2002). Inferences for generalized exponential distribution based on record statistics. Journal of Statistical Planning and Inference, 104, 339-350.   DOI
23 Raqab, M. Z. and Ahsanullah, M. (2001). Estimation of location and scale parameters of generalized exponential distribution based on order statistics. Journal of Statistical Computation and Simulation, 69, 109-123.   DOI
24 Raqab, M. Z. (2004). Generalized exponential distribution: Moments of order statistics. Statistics, 38, 29-41.   DOI
25 Sultan, K. S. and Moshref, M. E. (2000). Record values from generalized Pareto distribution and associated inference. Metrika, 51, 105-116.   DOI
26 Zheng, G. (2002). On the Fisher information matrix in type II censored data from the exponentiated exponential family. Biometrical journal, 44, 353-357.   DOI
27 Shawky, A. I. and Abu-Zinadah, H. H. (2008). Characterizations of the exponentiated Pareto distribution based on record values. Applied Mathematical Sciences, 2, 1283-1290.