Some Reliability Properties of Extropy and its Related Measures Using Quantile Function
DOI:
https://doi.org/10.6092/issn.1973-2201/9887Keywords:
Extropy, Quantile function, Hazard quantile function, Order statistics, Mean residual quantile functionAbstract
Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated.
References
M. ABBASNEJAD, N. R. ARGHAMI (2010). Renyi entropy properties of order statistics. Communications in Statistics—Theory and Methods, 40, no. 1, pp. 40–52.
H. ALIZADEH NOUGHABI, J. JARRAHIFERIZ (2019). On the estimation of extropy. Journal of Nonparametric Statistics, 31, no. 1, pp. 88–99.
B. C.ARNOLD, N. BALAKRISHNAN, H.N.NAGARAJA (1992). A First Course in Order Statistics, vol. 54. JohnWiley & Son, New York.
S. BARATPOUR, J. AHMADI, N. R. ARGHAMI (2008). Characterizations based on Renyi entropy of order statistics and record values. Journal of Statistical Planning and Inference, 138, no. 8, pp. 2544–2551.
H. DAVID, H. NAGARAJA (2003). Order Statistics. John Wiley & Sons, London, 3rd ed.
W. GILCHRIST (2000). Statistical Modelling with Quantile Functions. Chapman and Hall/CRC, Boca Raton, FL.
Z. GOVINDARAJULU (1977). A class of distributions useful in life testing and reliability with applications to nonparametric testing. In C. P.TSOKOS, I. SHIMI (eds.), The Theory and Applications of Reliability with Emphasis on Bayesian and Nonparametric Methods, Elsevier, pp. 109–129.
J. R. HOSKING (1992). Moments or L moments? An example comparing two measures of distributional shape. The American Statistician, 46, no. 3, pp. 186–189.
S. M. A. JAHANSHAHI, H. ZAREI, A. H. KHAMMAR (2019). On cumulative residual extropy. Probability in the Engineering and Informational Sciences, pp. 1–21.
J. JOSE, E.A. SATHAR (2019). Residual extropy of k-record values. Statistics & Probability Letters, 146, pp. 1–6.
S. KAYAL, M. R. TRIPATHY (2018). A quantile-based Tsallis-α divergence. Physica A: Statistical Mechanics and its Applications, 492, pp. 496–505.
A. S. KRISHNAN, S. M. SUNOJ, P. G. SANKARAN (2019). Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime. Metrika, 82, no. 1, pp. 17–38.
V. KUMAR, REKHA (2018). A quantile approach of Tsallis entropy for order statistics. Physica A: Statistical Mechanics and its Applications, 503, pp. 916–928.
F. LAD, G. SANFILIPPO (2015). Extropy: Complementary dual of entropy. Statistical Science, 30, no. 1, pp. 40–58.
N. N. MIDHU, P. G. SANKARAN, N. U. NAIR (2013). A class of distributions with the linear mean residual quantile function and its generalizations. Statistical Methodology, 15, pp. 1–24.
N. U. NAIR, P. G. SANKARAN (2009). Quantile-based reliability analysis. Communications in Statistics-Theory and Methods, 38, no. 2, pp. 222–232.
N. U. NAIR, P. G. SANKARAN, N. BALAKRISHNAN (2013). Quantile-Based Reliability Analysis. Springer Science & Business Media, New York.
N. U. NAIR, B. VINESHKUMAR (2011). Ageing concepts: An approach based on quantile function. Statistics & Probability Letters, 81, no. 12, pp. 2016–2025.
E. PARZEN (1979). Nonparametric statistical data modeling. Journal of the American Statistical Association, 74, no. 365, pp. 105–121.
G. QIU (2017). The extropy of order statistics and record values. Statistics & Probability Letters, 120, pp. 52–60.
G. QIU, K. JIA (2018). The residual extropy of order statistics. Statistics & Probability Letters, 133, pp. 15–22.
G.QIU, L.WANG, X.WANG (2019). On extropy properties of mixed systems. Probability in the Engineering and Informational Sciences, 33, no. 3, pp. 471–486.
M. Z. RAQAB, G. QIU (2018). On extropy properties of ranked set sampling. Statistics, pp. 1–15.
P. G. SANKARAN, S. M. SUNOJ (2017). Quantile-based cumulative entropies. Communications in Statistics-Theory and Methods, 46, no. 2, pp. 805–814.
P. G. SANKARAN, N. UNNIKRISHNAN NAIR (2009). Nonparametric estimation of hazard quantile function. Journal of Nonparametric Statistics, 21, no. 6, pp. 757–767.
M. SHAKED, J. G. SHANTHIKUMAR (2007). Stochastic Orders. Springer Science & Business Media, New York.
N. SREELAKSHMI, S. K. KATTUMANNIL, G. ASHA (2018). Quantile based tests for exponentiality against DMRQ and NBUE alternatives. Journal of the Korean Statistical Society, 47, no. 2, pp. 185–200.
S. M. SUNOJ, A. S. KRISHNAN, P. G. SANKARAN (2017). Quantile-based entropy of order statistics. Journal of the Indian Society for Probability and Statistics, 18, no. 1, pp. 1–17.
S. M. SUNOJ, A. S. KRISHNAN, P. G. SANKARAN (2018). A quantile-based study of cumulative residual Tsallis entropy measures. Physica A: Statistical Mechanics and its Applications, 494, pp. 410–421.
S. M. SUNOJ, P. G. SANKARAN (2012). Quantile based entropy function. Statistics & Probability Letters, 82, no. 6, pp. 1049–1053.
K. M.WONG, S.CHEN (1990). The entropy of ordered sequences and order statistics. IEEE Transactions on Information Theory, 36, no. 2, pp. 276–284.
J. YANG, W. XIA, T. HU (2018). Bounds on extropy with variational distance constraint. Probability in the Engineering and Informational Sciences, pp. 1–19.
H.-L. YU, C.-H. WANG (2013). Quantile-based Bayesian maximum entropy approach for spatiotemporal modeling of ambient air quality levels. Environmental Science & Technology, 47, no. 3, pp. 1416–1424.
S. ZAREZADEH, M. ASADI (2010). Results on residual Renyi entropy of order statistics and record values. Information Sciences, 180, no. 21, pp. 4195–4206.
W. J. ZIMMER, J. B. KEATS, F. WANG (1998). The Burr XII distribution in reliability analysis. Journal of Quality Technology, 30, no. 4, pp. 386–394.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
