Estimation of Dynamic Cumulative Past Entropy for Power Function Distribution


  • Enchakudiyil Ibrahim Abdul-Sathar University of Kerala, Thiruvananthapuram
  • Glory Sathyanesan Sathyareji University of Kerala, Thiruvananthapuram



Power function distribution, Bayes estimators, DCPE, Lindely approximation, Importance sampling, HPD credible interval


In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter power function distribution. Bayes estimators under different loss functions are obtained using Lindley approximation method and important sampling procedures. A real life data set and a Monte Carlo simulation are used to study the performance of the estimators derived in the article.


E. I. ABDUL-SATHAR, K. R. RENJINI, G. RAJESH, E. S. JEEVANAND (2015a). Bayes estimation of Lorenz curve and Gini-index for power function distribution. South African Statistical Journal, 49, no. 1, pp. 21–33.

E. I. ABDUL-SATHAR, K. R. RENJINI, G. RAJESH, E. S. JEEVANAND (2015b). Quasi-Bayesian estimation of Lorenz curve and Gini-index in the power model. Aligarh Journal of Statistics, 35, pp. 61–76.

S. B. BAGCHI, P. SARKAR (1986). Bayes interval estimation for the shape parameter of the power distribution. IEEE transactions on reliability, 35, no. 4, pp. 396–398.

F. BELZUNCE, J. CANDEL, J. M. RUIZ (1998). Ordering and asymptotic properties of residual income distributions. Sankhya: The Indian Journal of Statistics, Series B, 60,no. 2, pp. 331–348.

R. CALABRIA, G. PULCINI (1996). Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics-Theory and Methods, 25, no. 3, pp. 585–600.

M.-H. CHEN, Q.-M. SHAO (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, no. 1, pp. 69–92.

A. C. DAVISON, D. V.HINKLEY (1997). Bootstrap Methods and their Application, vol. 1. Cambridge University Press, New York.

A. DI CRESCENZO, M. LONGOBARDI (2002). Entropy-based measure of uncertainty in past lifetime distributions. Journal of Applied Probability, 39, no. 2, pp. 434–440.

A. DI CRESCENZO, M. LONGOBARDI (2004). A measure of discrimination between past lifetime distributions. Statistics & Probability Letters, 67, no. 2, pp. 173–182.

A. DI CRESCENZO, M. LONGOBARDI (2009). On cumulative entropies. Journal of Statistical Planning and Inference, 139, no. 12, pp. 4072–4087.

M. HUSS, P. HOLME (2007). Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks. IET Systems Biology, 1, no. 5, pp. 280–285.

D. V. LINDLEY (1980). Approximate Bayesian methods. Trabajos de Estadística Y de Investigación Operativa, 31, no. 1, pp. 223–245.

M. MENICONI, D. M. BARRY (1996). The power function distribution: A useful and simple distribution to assess electrical component reliability. Microelectronics Reliability, 36, no. 9, pp. 1207–1212.

A. A. OMAR, H. C. LOW (2012). Bayesian estimate for shape parameter from generalized power function distribution. Mathematical Theory and Modeling, 2, no. 12, pp. 1–7.

H. RAHMAN, M. K. SSSROY, A. R. BAIZID (2012). Bayes estimation under conjugate prior for the case of power function distribution. American Journal of Mathematics and Statistics, 2, no. 3, pp. 44–48.

C. E. SHANNON (1948). A mathematical theory of communication. Mobile Computing and Communications Review, 5, no. 1, pp. 3–55.

A. ZAKA, A. S. AKHTER (2014). Bayesian analysis of power function distribution using different loss functions. International Journal of Hybrid Information Technology, 7, no. 6, pp. 229–244.




How to Cite

Abdul-Sathar, E. I., & Sathyareji, G. S. (2018). Estimation of Dynamic Cumulative Past Entropy for Power Function Distribution. Statistica, 78(4), 319–334.