Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

  • Safeih Daneshi Department of Statistics, Shahrood University of Technology, Shahrood, Iran
  • Ahmad Nezakati Department of Statistics, Shahrood University of Technology, Shahrood, Iran
  • Saeid Tahmasebi Department of Statistics, Persian Gulf University, Bushehr, Iran
Keywords: Cumulative inaccuracy, Order statistics, Empirical approach.

Abstract

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results  such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

Author Biographies

Safeih Daneshi, Department of Statistics, Shahrood University of Technology, Shahrood, Iran
Department of Statistics, Shahrood University of Technology, Shahrood, Iran Bushehr University of Medical Sciences, Bushehr, Iran
Ahmad Nezakati, Department of Statistics, Shahrood University of Technology, Shahrood, Iran
Department of Statistics, Shahrood University of Technology, Shahrood, Iran
Saeid Tahmasebi, Department of Statistics, Persian Gulf University, Bushehr, Iran
Department of Statistics, Persian Gulf University, Bushehr, Iran

References

B.C. Arnold, N. Balakrishnan, and H. N. Nagaraja, A first course in order statistics, John Wiley, New York, 1992.

S. Baratpour, Characterizations based on cumulative residual entropy of first-order statistics, Communications in Statistics-Theory and Methods, vol. 39, no. 20, pp. 3645-3651, 2010.

C. Cali, M. Longobardi, and J. Navarro, Properties for generalized cumulative past measures of information, Probability in the Engineering and Informational Sciences, pp. 1-20, 2018.

S. Danshi, A.Nezakati, and S, Tahmasebi, On weighted cumulative past (residual) inaccuracy for record values, Journal of Inequalities and Applications, vol. 2019, no. 1, pp.134, 2019.

M. Eskandarzadeh, A. Di Crescenzo, and S, Tahmasebi, Cumulative measure of inaccuracy and mutual information in k-th lower record values, Mathematics, vol. 7, no. 2, pp.175, https://doi.org/10.3390/math7020175, 2019.

A. Di Crescenzo, and M. Longobardi, On weighted residual and past entropies, Scientiae Mathematicae Japonicae, vol. 64, no. 2,pp. 255-266, 2006.

A. Di Crescenzo, and M. Longobardi, On cumulative entropies, Journal of Statistical Planning and Inference, vol. 139, pp. 4072-4087, 2009.

R. C. Gupta, and S. N. U. A. Kirmani, Characterization based on convex conditional mean function, Journal of Statistical Planning and Inference, vol. 138, no. 4, pp. 964-970, 2008.

S. Kayal, On weighted generalized cumulative residual entropy of order n, Methodology and Computing in Applied Probability,DOI 10.1007/s11009-017-9569-0, pp. 1-17, 2017.

S. Kayal, and R. Moharana, On weighted measures of cumulative entropy, International Journal of Mathematics and Statistics, vol.18, no. 3, pp. 26-46, 2017.

V. Kumar, and H. C. Taneja, Dynamic cumulative residual and past inaccuracy measures, J. Stat. Theory Appl, vol. 14, no. 4, pp.399-412, 2015.

F. Misagh, and G.H. Yari, On weighted interval entropy, Statistics and probability letters, vol. 81, no.2, pp. 188-194, 2011.

J. Navarro, Y. del Aguila and M. Asadi, Some new results on the cumulative residual entropy, Journal of Statistical Planning and Inference, vol. 140, pp. 310-322, 2010.

R. Pyke, Spacings, Journal of Royal Statistical Society, Series B, vol. 27, no. 3, pp. 395-449, 1965.

M. Rao, More on a new concept of entropy and information,Journal of Theoretical Probability, vol. 18, pp. 967-981, 2005.

M. Rao, Y. Chen, B. C. Vemuri, and F. Wang, Cumulative Residual Entropy: A New Measure of Information, IEEE Trans Inf Theory,vol. 50, no. 6, pp. 1220-1228, 2004.

M. Shaked, and J. G. Shanthikumar, Stochastic orders, Springer Science and Business Media, 2007.

C. E. Shannon, A mathematical theory of communication, Bell Syst. Tec. J, vol. 27, no. 3, pp. 379-432, 1948.

S. Tahmasebi, and S. Daneshi, Measures of inaccuracy in record values, Commun. Stat., Theory Methods, vol. 47, no. 24, pp.6002-6018, 2018.

S. Tahmasebi, A.Nezakati, and S. Daneshi, Results on cumulative measure of inaccuracy in record values, J. Stat. Theory Appl, vol.17, no. 1, pp. 15-28, 2018.

R. Thapliyal, and H. C. Taneja, On residual inaccuracy of order statistics, Statist. Probab. Lett, vol. 97, pp. 125-131, 2015.

V, Zardasht, Results on relative mean residual life and relative cumulative residual entropy, Statistics, Optimization and Information Computing, vol. 7, no. 1, pp. 150-159, 2019.

Published
2020-02-17
How to Cite
Daneshi, S., Nezakati, A., & Tahmasebi, S. (2020). Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics. Statistics, Optimization & Information Computing, 8(1), 110-126. https://doi.org/10.19139/soic-2310-5070-695
Section
Research Articles