References
- Abdul-Sathar, E., G. Rajesh, and K. M. Nair. 2010. Bivariate geometric vitality function and some characterization results. Calcutta Statistical Association Bulletin 62 (3-4):207–28. doi: 10.1177/0008068320100305.
- Ahmad, I., and P. E. Lin. 1976. A nonparametric estimation of the entropy for absolutely continuous distributions (corresp.). IEEE Transactions on Information Theory 22 (3):372–75. doi: 10.1109/TIT.1976.1055550.
- Ahmad, I. A., and P. E. Lin. 1977. Nonparametric estimation of a vector-valued bivariate failure rate. The Annals of Statistics 5 (5):1027–38. doi: 10.1214/aos/1176343957.
- Ahmed, N. A., and D. Gokhale. 1989. Entropy expressions and their estimators for multivariate distributions. IEEE Transactions on Information Theory 35 (3):688–92. doi: 10.1109/18.30996.
- Asadi, M., and N. Ebrahimi. 2000. Residual entropy and its characterizations in terms of hazard function and mean residual life function. Statistics & Probability Letters 49 (3):263–69. doi: 10.1016/S0167-7152(00)00056-0.
- Asadi, M., N. Ebrahimi, G. Hamedani, and E. S. Soofi. 2004. Maximum dynamic entropy models. Journal of Applied Probability 41 (2):379–90. doi: 10.1239/jap/1082999073.
- Belzunce, F., A. Guillamón, J. Navarro, and J. Ruiz. 2001. Kernel estimation of residual entropy. Communications in Statistics - Theory and Methods 30 (7):1243–55. doi: 10.1081/STA-100104743.
- Belzunce, F., J. Navarro, J. M. Ruiz, and Y. del Aguila. 2004. Some results on residual entropy function. Metrika 59 (2):147–61. doi: 10.1007/s001840300276.
- Cacoullos, T. 1966. Estimation of a multivariate density. Annals of the Institute of Statistical Mathematics 18 (1):179–89. doi: 10.1007/BF02869528.
- Darbellay, G. A., and I. Vajda. 2000. Entropy expressions for multivariate continuous distributions. IEEE Transactions on Information Theory 46 (2):709–12. doi: 10.1109/18.825848.
- Dmitriev, Y. G., and F. Tarasenko. 1973. On estimation of functionals of the probability density function and its derivatives. Teoriya Veroyatnostei i ee Primeneniya 18 (3):662–68.
- Ebrahimi, N. 1996. How to measure uncertainty in the residual life time distribution. Sankhyā: The Indian Journal of Statistics, Series A 58: 48–56.
- Ebrahimi, N., S. Kirmani, and E. S. Soofi. 2007. Multivariate dynamic information. Journal of Multivariate Analysis 98 (2):328–49. doi: 10.1016/j.jmva.2005.08.004.
- Ebrahimi, N., and F. Pellerey. 1995. New partial ordering of survival functions based on the notion of uncertainty. Journal of Applied Probability 32 (1):202–11. doi: 10.2307/3214930.
- Kulkarni, H. V., and R. Rattihalli. 2002. Nonparametric estimation of a bivariate mean residual life function. Journal of the American Statistical Association 97 (459):907–17. doi: 10.1198/016214502388618690.
- Muliere, P., G. Parmigiani, and N. G. Polson. 1993. A note on the residual entropy function. Probability in the Engineering and Informational Sciences 7 (3):413–20. doi: 10.1017/S0269964800003016.
- Nadarajah, S., and K. Zografos. 2005. Expressions for Rényi and Shannon entropies for bivariate distributions. Information Sciences 170 (2-4):173–89. doi: 10.1016/j.ins.2004.02.020.
- Nair, K., and G. Rajesh. 1998. Characterization of probability distributions using the residual entropy function. Journal of the Indian Statistical Association 36:157–66.
- Rajesh, G., E. Abdul-Sathar, R. Maya, and K. M. Nair. 2015. Nonparametric estimation of the residual entropy function with censored dependent data. Brazilian Journal of Probability and Statistics 29 (4):866–77. doi: 10.1214/14-BJPS250.
- Rajesh, G., and K. Nair. 2000. Residual entropy of conditional distributions. Statistical Methods 2 (1):72–80.
- Rajesh, G., A. Sathar, and K. Nair. 2009. Bivariate extension of residual entropy and some characterization results. Journal of the Indian Statistical Association 47:91–107.
- Sathar, A., K. Nair, and G. Rajesh. 2010. Generalized bivariate residual entropy function and some characterization results. South African Statistical Journal 44:1–18.
- Shannon, C. E. 1948. A mathematical theory of communication. The Bell System Technical Journal 27 (3):379–423. doi: 10.1002/j.1538-7305.1948.tb01338.x.
- Sheather, S. J., and M. C. Jones. 1991. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society: Series B (Methodological) 53 (3):683–90.
- Smaldino, P. E. 2013. Measures of individual uncertainty for ecological models: Variance and entropy. Ecological Modelling 254:50–53. doi: 10.1016/j.ecolmodel.2013.01.015.
- Spierdijk, L. 2008. Nonparametric conditional hazard rate estimation: A local linear approach. Computational Statistics & Data Analysis 52 (5):2419–34. doi: 10.1016/j.csda.2007.08.007.
- Vasicek, O. 1976. A test for normality based on sample entropy. Journal of the Royal Statistical Society: Series B (Methodological) 38 (1):54–59.
- Zografos, K. 1999. On maximum entropy characterization of Pearson’s type II and VII multivariate distributions. Journal of Multivariate Analysis 71 (1):67–75. doi: 10.1006/jmva.1999.1824.