Main Article Content



Burbea and Rao [3,4] and Sgarro [11] established an inequality between two famous divergence measures i.e., Jeffreys [6] invariant function ($J$-divergence) and Sibson's [13] information radius ($R$-divergence). Taneja [14,16] generalized both these divergences ($J$ and $R$) having two scalar parameters. In this paper, we have extended the inequality between the $R$ and $J$-divergences for two parametric cases. For one parametric generalizations of $R$ and $J$-divergences, the generalized inequalities are improved.

Article Details

How to Cite
TANEJA, I. J., PARDO, L., & MENÉNDEZ, M. L. (1991). SOME INEQUALITIES AMONG GENERALIZED DIVERGENCE MEASURES. Tamkang Journal of Mathematics, 22(2), 175–185.


Burbea, "J -Divergences and Related Concepts", Encyclopedia of Statistical Sciences. 4 (1983), 290-296.

Burbea, J., "The Convexity with Respect to Gaussian Distribution of Divergences of Order Q", Utilitas Mathematica. 26 (1984), 171-192.

Burbea, J. and C. R. Rao, "On the convexity of some divergence measures based on entropy functions", IEEE Trans. on Information Theory. IT-28 (1982), 489-495.

Burbea, J. and C. R. Rao, "Entropy Differential Metric, Distance and Divergence Measures in Probability Spaces: A Unified Approach", J. Multi. Analy. 12 (1982), 575-596.

Capocelli, R. M. and I. J. Taneja, "Divergence Measures and Error Bounds", Proc. IEEE lnterant. Conj. Syst., Man & Cyhern., Halifax, Canada, October 9-12 (1984), 43-46.

H. Jeffreys, "An Invariant form for the Prior Probability in Estimation Problems". Proc. Royal Soc., Ser A. 186 (1946), 453-561.

Kullback, S. and A. Leibler, "On the information and sufficiency". Ann. Math. Statist., 22 (1951), 79-86.

Menendez, M. L., I. J. Taneja and L. Pardo, "On Unified (r,s)-Jensen Difference Divergence Mea- sures", Communicated.

Pardo, L., D. Morales, and I. J. Taneja, "Generalized Jensen Difference Divergence Measures and Fisher Measure of Information", Communicated. ·

Rathie, P. N. and L. T. Sheng, "The J-Divergence of Order Q 11, J. Comb. Inform. & Syst. Sci., 6 (1981), 197-205.

Sgarro, A., Infonnational divergence and the dissimilarity of probability distributions, Estratto di Calcolo, XVIII (1981), 293-302.

Shannon, C. E., "A Mathematical theory of Communication", Bell. Syst. Tech. J., 27 (1948), 379-423.

Sibson, R., "Information Radius", Z. Wars. und verw Geb., 14 (1969), 149-160.

Taneja, I. J., "On a Characterization of J-Divergence and its Generalizations", J. Comb. Inform & Syst. Sci., 8 (1983), 206-212.

Taneja, I. J., "Statistical aspects of divergence measures", J. Statist Planning & Inference, 16 (1987), 136-145.

Taneja, I. J., "On Generalized Information Measures and their Applications", Ad. Electronics and Electron Physics, 76 (1989), 327-413.

Taneja, I. J., "Bounds on the Probability of Error in Terms of Information Radius", Information Sciences, Vol. 46 .

Taneja, I. J., L. Pardo and M. L. Menendez,"On unified (r,s)-J-divergence measures",Information Sciences (under revision).

Taneja, I. J., L. Pardo and D. Morales, "Generalized Jensen Difference Divergence Measures and Comparison of Experiments", Communicated.