A new two-parametric weighted generalized inaccuracy measure

A. Fayaz; M. A. K. Baig

doi:10.2478/jamsi-2023-0010

.blurhash-client-img { display: none !important; }

A new two-parametric weighted generalized inaccuracy measure

Journal of Applied Mathematics, Statistics and Informatics

Volume 19 (2023): Issue 2 (December 2023)

By: A. Fayaz and M. A. K. Baig

Open Access

|Jan 2024

Abstract

In this article, we present a novel approach to measuring inaccuracy, introducing a two-parametric weighted generalized inaccuracy measure of order α and type β, along with its residual version. Our proposed measure depends on the proportional hazard rate model (PHRM) to uniquely determine the survival function, and we have derived a characterization result for this measure. Through our analysis under the PHRM framework, we have studied various properties of the proposed measure and their interrelationships.

References

ASOKAN, M. V., AND SANKARAN, P. G. (2014). Parametric regression models using reversed hazard rates. Journal of Probability and Statistics, 1-5. https://doi.org/10.1155/2014/645719
Search in Google Scholar Back to article
BELIS, M., AND GUIASU, S. (1968). A quantitative-qualitative measure of information in cybernetic systems (Corresp.). IEEE Transactions on Information Theory, 14(4), 593-594.
Search in Google Scholar Back to article
CALÌ, C., LONGOBARDI, M., AND NAVARRO, J. (2020). Properties for generalized cumulative past measures of information. Probability in the Engineering and Informational Sciences, 34(1), 92-111.
Search in Google Scholar Back to article
DI CRESCENZO, A. (2000). Some results on the proportional reversed hazards model. Statistics and probability letters, 50(4), 313-321.
Search in Google Scholar Back to article
DI CRESCENZO, A., AND LONGOBARDI, M. (2007). On weighted residual and past entropies. arXiv preprint math/0703489.
Search in Google Scholar Back to article
DI CRESCENZO A., KAYAL S., TOOMAJ A. (2019) A past inaccuracy measure based on the reversed relevation transform. Metrika 82:607–631
Search in Google Scholar Back to article
EBRAHIMI, N., SOOFI, E. S., AND SOYER, R. (2010). Information measures in perspective. International Statistical Review, 78(3), 383-412.
Search in Google Scholar Back to article
GUPTA, R. C., AND GUPTA, R. D. (2007). Proportional reversed hazard rate model and its applications. Journal of statistical planning and inference, 137(11), 3525-3536.
Search in Google Scholar Back to article
KUMAR, V., SRIVASTAVA, R., AND TANEJA, H. C. (2010). Length biased weighted residual inaccuracy measure. Metron, 68, 153-160.
Search in Google Scholar Back to article
KAYAL S., SUNOJ S. M., RAJESH G. (2017) On dynamic generalized measures of inaccuracy. Statistica 77:133–148
Search in Google Scholar Back to article
KUNDU, C., NANDA, A. K., AND MAITI, S. S. (2010). Some distributional results through past entropy. Journal of statistical planning and inference, 140(5), 1280-1291.
Search in Google Scholar Back to article
KERRIDGE, D. F. (1961). Inaccuracy and inference. Journal of the Royal Statistical Society. Series B (Methodological), 184-194.
Search in Google Scholar Back to article
KAPUR, J. N. (1968, August). Information of order α and type β . In Proceedings of the Indian Academy of Sciences-Section A (Vol. 68, No. 2, pp. 65-75). New Delhi: Springer India.
Search in Google Scholar Back to article
KAYAL, S., SUNOJ, S. M.: Generalized Kerridge’s inaccuracy measure for conditionally specified models. Commun. Stat., Theory Methods 46 (2017), 8257–8268.
Search in Google Scholar Back to article
KAYAL, S., MOHARANA, R. AND SUNOJ, S. M. (2019). Quantile-based study of (dynamic) inaccuracy measures, Prob. in the Eng. and Inf. Sci. doi.org/10.1017/S0269964819000019.
Search in Google Scholar Back to article
KUNDU, D., AND GUPTA, R. D. (2010). A class of bivariate models with proportional reversed hazard marginals. Sankhya B, 72(2), 236-253.
Search in Google Scholar Back to article
KUNDU, C., DI CRESCENZO, A., AND LONGOBARDI, M. (2016). On cumulative residual (past) inaccuracy for truncated random variables. Metrika, 79(3), 335-356.
Search in Google Scholar Back to article
MULAYATH VARIYATH, A., AND SANKARAN, P. G. (2014). Parametric regression models using reversed hazard rates. Journal of Probability and Statistics, 2014.
Search in Google Scholar Back to article
NATH, P. (1968). Inaccuracy and coding theory. Metrika, 13(1), 123-135.
Search in Google Scholar Back to article
RÉNYI, A. (1961, January). On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics (Vol. 4, pp. 547-562). University of California Press.
Search in Google Scholar Back to article
SANKARAN, P. G., AND GLEEJA, V. L. (2008). Proportional reversed hazard and frailty models. Metrika, 68, 333-342.
Search in Google Scholar Back to article
SENGUPTA, D. AND NANDA, A.K. (2011). The proportional reversed hazards regression model. Journal of Statistical Theory and Applications, 18(4), 461-476.
Search in Google Scholar Back to article
SHANNON, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3), 379-423.
Search in Google Scholar Back to article
TANEJA, H. C., KUMAR, V., AND SRIVASTAVA, R. (2009). A dynamic measure of inaccuracy between two residual lifetime distributions. In International Mathematical Forum (Vol. 4, No. 25, pp. 1213-1220).
Search in Google Scholar Back to article
UNNIKRISHNAN N.N., SANKARAN, P.G. AND SUNOJ, S.M. (2018). Some properties of proportional reversed hazards model based on quantile functions. International Journal of Reliability, Quality and Safety Engineering. https://doi.org/10.1142/S0218539319500116
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/jamsi-2023-0010 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180

Journal RSS Feed

Language: English

Page range: 57 - 73

Published on: Jan 6, 2024

Published by: University of Ss. Cyril and Methodius in Trnava

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Characterization results,

Distribution function,

Inaccuracy measure,

Renyi entropy,

Shannon entropy,

Weighted inaccuracy measure

Related subjects:

Computer sciences,

Information technology,

Mathematics,

Logic and set theory,

Probability and statistics,

Applied mathematics

© 2024 A. Fayaz, M. A. K. Baig, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 19 (2023): Issue 2 (December 2023)