Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T09:17:22.377Z Has data issue: false hasContentIssue false
  • English
  • Français

QUANTILE-BASED STUDY OF (DYNAMIC) INACCURACY MEASURES

Published online by Cambridge University Press:  22 February 2019

Suchandan Kayal ,
Rajesh Moharana  and
S. M. Sunoj
Suchandan Kayal
Affiliation:
Department of Mathematics, National Institute of Technology Rourkela, Rourkela - 769008, India E-mail: [email protected]; [email protected]
Rajesh Moharana
Affiliation:
Department of Mathematics, National Institute of Technology Rourkela, Rourkela - 769008, India E-mail: [email protected]; [email protected]
S. M. Sunoj
Affiliation:
Department of Statistics, Cochin University of Science and Technology, Cochin - 682022, India E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In the present communication, we introduce quantile-based (dynamic) inaccuracy measures and study their properties. Such measures provide an alternative approach to evaluate inaccuracy contained in the assumed statistical models. There are several models for which quantile functions are available in tractable form, though their distribution functions are not available in explicit form. In such cases, the traditional distribution function approach fails to compute inaccuracy between two random variables. Various examples are provided for illustration purpose. Some bounds are obtained. Effect of monotone transformations and characterizations are provided.

Keywords

boundscharacterizationKerridge's inaccuracy measurelikelihood ratio quantile orderquantile function
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 2 , April 2020 , pp. 183 - 199
Copyright
Copyright © Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Baratpour, S. & Khammar, A.H. (2017). A quantile-based generalized dynamic cumulative measure of entropy. Communications in Statistics-Theory and Methods, 47: 3104–3117.CrossRefGoogle Scholar
2Block, H.W., Savits, T.H., & Singh, H. (1998). The reversed hazard rate function. Probability in the Engineering and Informational Sciences, 12(1): 69–90.CrossRefGoogle Scholar
3Di Crescenzo, A. & Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distributions. Journal of Applied Probability, 39(2): 434–440.CrossRefGoogle Scholar
4Ebrahimi, N. (1996). How to measure uncertainty in the residual life time distribution. Sankhya: The Indian Journal of Statistics, Series A, 58(1): 48–56.Google Scholar
5Gilchrist, W. (2000). Statistical modelling with quantile functions. Boca Raton, FL: Chapman and Hall/CRC.CrossRefGoogle Scholar
6Govindarajulu, Z. (1977). A class of distributions useful in life testing and reliability with applications to nonparametric testing. The Theory and Applications of Reliability with Emphasis on Bayesian and Nonparametric Methods, 1, 109–129.CrossRefGoogle Scholar
7Kayal, S. (2017). Quantile-based Chernoff distance for truncated random variables. Communications in Statistics-Theory and Methods, 47: 4938–4957.CrossRefGoogle Scholar
8Kayal, S. & Tripathy, M.R. (2018). A quantile-based Tsallis-α divergence. Physica A: Statistical Mechanics and its Applications, 492, 496–505.CrossRefGoogle Scholar
9Kerridge, D.F. (1961). Inaccuracy and inference. Journal of the Royal Statistical Society. Series B (Methodological), 23, 184–194.CrossRefGoogle Scholar
10Khammar, A.H. & Jahanshahi, S.M.A. (2018). Quantile based Tsallis entropy in residual lifetime. Physica A: Statistical Mechanics and its Applications, 492, 994–1006.CrossRefGoogle Scholar
11Kumar, V., Taneja, H.C., & Srivastava, R. (2011). A dynamic measure of inaccuracy between two past lifetime distributions. Metrika, 74(1): 1–10.CrossRefGoogle Scholar
12Kundu, C. & Nanda, A.K. (2015). Characterizations based on measure of inaccuracy for truncated random variables. Statistical Papers, 56(3): 619–637.CrossRefGoogle Scholar
13Nair, N.U. & Gupta, R.P. (2007). Characterization of proportional hazard models by properties of information measures. International Journal of Statistical Sciences, 6, 223–231.Google Scholar
14Nair, N.U., Sankaran, P.G., & Balakrishnan, N. (2013). Quantile-based reliability analysis. New York: Springer Science+Business Media.CrossRefGoogle Scholar
15Nair, N.U., Sankaran, P.G., & Sunoj, S.M. (2018). Proportional hazards model with quantile functions. Communications in Statistics-Theory and Methods, 47: 4170–4723.CrossRefGoogle Scholar
16Nath, P. (1968). Entropy, inaccuracy and information. Metrika, 13(1): 136–148.CrossRefGoogle Scholar
17Parzen, E. (1979). Nonparametric statistical data modeling. Journal of the American statistical association, 74(365): 105–121.CrossRefGoogle Scholar
18Qiu, G. (2018). Further results on quantile entropy in the past lifetime. Probability in the Engineering and Informational Sciences, 1–14.Google Scholar
19Sankaran, P.G., Sunoj, S.M., & Nair, N.U. (2016). Kullback-Leibler divergence: a quantile approach. Statistics & Probability Letters, 111, 72–79.CrossRefGoogle Scholar
20Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.CrossRefGoogle Scholar
21Sunoj, S.M. & Sankaran, P.G. (2012). Quantile based entropy function. Statistics & Probability Letters, 82(6): 1049–1053.CrossRefGoogle Scholar
22Sunoj, S., Sankaran, P.G., & Nanda, A.K. (2013). Quantile based entropy function in past lifetime. Statistics & Probability Letters, 83(1): 366–372.CrossRefGoogle Scholar
23Sunoj, S.M., Sankaran, P.G., & Nair, N.U. (2017). Quantile-based reliability aspects of Renyi's information divergence measure. Journal of the Indian Society for Probability and Statistics, 18(2): 267–280.CrossRefGoogle Scholar
24Sunoj, S.M., Sankaran, P.G., & Nair, N.U. (2018). Quantile-based cumulative Kullback-Leibler divergence. Statistics, 52(1): 1–17.CrossRefGoogle Scholar
25Sunoj, S.M., Krishnan, A.S., & Sankaran, P.G. (2018). A quantile-based study of cumulative residual Tsallis entropy measures. Physica A: Statistical Mechanics and its Applications, 494, 410–421.CrossRefGoogle Scholar
26Taneja, H.C., Kumar, V., & Srivastava, R. (2009). A dynamic measure of inaccuracy between two residual lifetime distributions. International Mathematical Forum, 4(25): 1213–1220.Google Scholar