From Quantile Functions to Subquantile Functions and Their Applications

References

[1] C. Acerbi, Spectral measures of risk: A coherent representation of subjective risk aversion, J. Banking Finance 26 (2002), no. 7, 1505–1518. 10.1016/S0378-4266(02)00281-9Search in Google Scholar

[2] B. Al-Zahrani and M. Al-Sobhi, On some properties of the reversed variance residual lifetime, Int. J. Statist. Probab. 4 (2015), no. 2, 24–32. 10.5539/ijsp.v4n2p24Search in Google Scholar

[3] S. Baratpour and A. H. Khammar, A quantile-based generalized dynamic cumulative measure of entropy, Comm. Statist. Theory Methods 47 (2018), no. 13, 3104–3117. 10.1080/03610926.2017.1348520Search in Google Scholar

[4] H. W. Block, T. H. Savits and H. Singh, The reversed hazard rate function, Probab. Engrg. Inform. Sci. 12 (1998), no. 1, 69–90. 10.1017/S0269964800005064Search in Google Scholar

[5] M. Denuit, J. Dhaene, M. Goovaerts and R. Kaas, Actuarial Theory for Dependent Risks: Measures, Orders and Models, John Wiley & Sons, Chichester, 2006. 10.1002/0470016450Search in Google Scholar

[6] A. Di Crescenzo and M. Longobardi, Entropy-based measure of uncertainty in past lifetime distributions, J. Appl. Probab. 39 (2002), no. 2, 434–440. 10.1239/jap/1025131441Search in Google Scholar

[7] A. Di Crescenzo and M. Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 (2009), no. 12, 4072–4087. 10.1016/j.jspi.2009.05.038Search in Google Scholar

[8] A. Di Crescenzo and A. Toomaj, Extension of the past lifetime and its connection to the cumulative entropy, J. Appl. Probab. 52 (2015), no. 4, 1156–1174. 10.1239/jap/1450802759Search in Google Scholar

[9] W. Gilchrist, Statistical Modelling with Quantile Functions, Chapman and Hall/CRC, New York, 2000. 10.1201/9781420035919Search in Google Scholar

[10] A. V. Lebedev, Exact and conditional bounds for generalized cumulative entropy, Reliab. Theory Appl. 19 (2024), no. 1(77), 440–447. Search in Google Scholar

[11] F. Misagh, Y. Panahi, G. Yari and R. Shahi, Weighted cumulative entropy and its estimation, 2011 IEEE International Conference on Quality and Reliability, IEEE Press, Piscataway (2011), 477–480. 10.1109/ICQR.2011.6031765Search in Google Scholar

[12] D. Mukherjee and M. V. Ratnaparkhi, On the functional relationship between entropy and variance with related applications, Comm. Statist. Theory Methods 15 (1986), no. 1, 291–311. 10.1080/03610928608829122Search in Google Scholar

[13] N. U. Nair and P. G. Sankaran, Quantile-based reliability analysis, Comm. Statist. Theory Methods 38 (2009), no. 1–2, 222–232. 10.1080/03610920802187430Search in Google Scholar

[14] N. U. Nair and P. G. Sankaran, Quantile-based lower partial moments and their applications, Amer. J. Math. Manag. Sci. 33 (2011), no. 3, 255–276. Search in Google Scholar

[15] N. U. Nair, P. G. Sankaran and N. Balakrishnan, Quantile-Based Reliability Analysis. With a foreword by J. R. M. Hosking, Statistics for Industry and Technology, Birkhäuser/Springer, New York, 2013. 10.1007/978-0-8176-8361-0_2Search in Google Scholar

[16] N. U. Nair, P. G. Sankaran and B. V. Kumar, Total time on test transforms of order n and their implications in reliability analysis, J. Appl. Probab. 45 (2008), no. 4, 1126–1139. 10.1239/jap/1231340238Search in Google Scholar

[17] N. U. Nair, S. M. Sunoj and S. Subhash, Superquantile function of order n and their applications in reliability and entropy, Statist. Probab. Lett. 225 (2025), Paper No. 110457. 10.1016/j.spl.2025.110457Search in Google Scholar

[18] N. U. Nair and B. Vineshkumar, Cumulative entropy and income analysis, Stoch. Qual. Control 37 (2022), no. 2, 165–179. 10.1515/eqc-2022-0012Search in Google Scholar

[19] J. Navarro, Introduction to System Reliability Theory, Springer, Cham, 2022. 10.1007/978-3-030-86953-3Search in Google Scholar

[20] E. Parzen, Nonparametric statistical data modeling, J. Amer. Statist. Assoc. 74 (1979), no. 365, 105–131. 10.2307/2286734Search in Google Scholar

[21] P. G. Sankaran and S. M. Sunoj, Quantile-based cumulative entropies, Comm. Statist. Theory Methods 46 (2017), no. 2, 805–814. 10.1080/03610926.2015.1006779Search in Google Scholar

[22] P. K. Sen, The Gini coefficient and poverty indexes: some reconciliations, J. Amer. Statist. Assoc. 81 (1986), no. 396, 1050–1057. 10.1080/01621459.1986.10478372Search in Google Scholar

[23] M. Shaked and J. G. Shanthikumar, Stochastic Orders, Springer Ser. Statist., Springer, New York, 2007. 10.1007/978-0-387-34675-5Search in Google Scholar

[24] S. Tahmasebi and H. Parsa, Notes on cumulative entropy as a risk measure, Stoch. Qual. Control 34 (2019), no. 1, 1–7. 10.1515/eqc-2018-0019Search in Google Scholar

[25] A. Toomaj and A. Di Crescenzo, Generalized entropies, variance and applications, Entropy 22 (2020), no. 6, Paper No. 709. 10.3390/e22060709Search in Google Scholar PubMed PubMed Central

[26] A. D. Wyner and J. Ziv, On communication of analog data from a bounded source space, Bell System Tech. J. 48 (1969), 3139–3172. 10.1002/j.1538-7305.1969.tb01740.xSearch in Google Scholar

[27] B. Zheng, Poverty orderings, J. Econom. Surveys 14 (2000), no. 4, 427–466. 10.1111/1467-6419.00117Search in Google Scholar