Author(s)

Rifat Nisa ¹, M.A.K Baig ¹

Affiliation(s)

¹ P.G. Department of Statistics, University of Kashmir, Srinagar-190006, India

Corresponding Author

Rifat Nisa

ABSTRACT

The Quantile based entropy measure own a few precise properties than its distribution function technique. In this article, the idea of quantile based Bilal’s and Baig’s uncertainty measure is prolonged for order statistics for residual and past lifetimes and have a look at their properties, this two parametric entropy measure characterizes the distribution characteristic uniquely. A few characterization results of generalized residual entropy of order statistics and monotonicity property is likewise mentioned.

KEYWORDS

Shannon’s Entropy; Order Statistics; Quantile function; Residual Entropy; Bilal’s and Baig’s uncertainty measure.

CITE THIS PAPER

Rifat Nisa and M.A.K Baig, Characterization Results based on Quantile version of Two Parametric Generalized Entropy of Order Statistics. Journal of Probability and Mathematical Statistics (2019) Vol. 1: 1-17.

REFERENCES

[1] Arghami, N. R., Abbasnejad, M. (2011). Renyi entropy properties of order statistics. Communications in Statistics-Theory and Methods 40, 40-52.
[2] Arnold, B. C., Balakrishnan, N., Nagaraja, H. N. (1992). A First Course in Order Statistics, New York, John Wiley and Sons.
[3] Bhat B., Baig M.A.K. (2019). A Shift-Dependent generalized doubly truncated (interval) information measure and its properties. International Scientific Research organization for Science, Engineering and technology. 6, 282-293.
[4] Baratpour, S., Khammar, A. (2015). Results on Tsallis entropy of order statistics and recorded values. ISTATISTIK: Journal of the Turkish Statistical Association 8(3), 60-73.
[5] Baratpour, S., Khammar, A. (2016). Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons. J. Statist. Res. Iran 13, 25-41.
[6] David, H. A., Nagaraja, H. N. (2003). Order Statistics, New York, Wiley.
[7] Di Crescenzo, A., Longobardi, M., 2002. Entropy-based measure of uncertainty in past lifetime distributions. Journal of Applied Probability 39, 434-440.
[8] Ebrahimi, N., (1996). How to measure uncertainty in the residual lifetime distribution. Sankhya Ser. A 58, 4856.
[9] Ebrahimi, N., Soofi, E. S., Zahedi, H. (2004). Information properties of order statistics and spacings. IEEE Transactions on Information Theory 50 (1), 177-183.
[10] Gilchrist, W. (2000). Statistical modelling with quantile functions. Chapman and Hall/CRC, Boca Raton, FL.
[11] Govindarajulu, Z. (1977). A class of distributions useful in lifetesting and reliability with applications to nonparametric testing. In: C.P. Tsokos, I.N. Shimi (eds.) Theory and Applications of Reliability, vol. 1, 109-130. Acad. Press, New York.
[12] Hankin, R. K. S., Lee, A. (2006). A new family of non-negative distributions. Austral. N.Z. J. Statist. 48, 67-78.
[13] Kayal, S., M. R., Tripathy (2017). A quantile-based Tsallis-_ divergence. Physica A: Statistical Mechanics and its Applications 492, 496-505.
[14] Kullback, S. (1959). Information Theory and Statistics, Wiley, New York.
[15] Kumar, V. Taneja, H. C. (2011). A Generalized Entropy-Based Residual Lifetime Distributions. International Journal of Biomathematics 4(2), 171-184.
[16] Kumar, V. Rani, R. (2017). Quantile based Tsallis entropy in residual and Inactivity time. Bulletin of Calcutta Mathematical Society 109(4) 275-294.
[17] Nanda, A. K., Paul, P. (2006). Some results on generalized residual entropy. Information Sciences 176, 27-47.
[18] Nair, N. U., Sankaran, P. G. (2009). Quantile based reliability analysis. Communications in Statistics Theory and Methods 38, 222-232.
[19] Nair, N. U., Sankaran, P. G., Vinesh Kumar, B. (2011). Modelling lifetimes by quantile functions using Parzens score function. Statistics 1, 113.
[20] Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27,379423.
[21] Sunoj, S. M., Krishnan, A. S., Sankaran, P. G. (2017). Quantile based entropy of order statistics. Journal of the Indian Society for Probability and Statistics 18(1), 1-17.
[22] Sunoj, S. M., Sankaran, P. G. (2012). Quantile based entropy function. Statistics and Probability Letters 82, 1049-1053.
[23] Sunoj, S. M., Sankaran, P. G., Nanda, A. K. (2013). Quantile based entropy function in past lifetime. Statistics and Probability Letters 83, 366-372.
[24] Thapliyal, R., Taneja, H. C., Kumar, V. (2015). Characterization results based on nonadditive entropy of order statistics. Physica -A Statistical Mechanics and its Applications 417, 297-303.
[25] Van Staden, P. J., Loots, M. R. (2009). L-moment estimation for the generalized lambda distribution. Third Annual ASEARC Conference, New Castle, Australia.

Sponsors, Associates, and Links

---

• International Journal of Power Engineering and Engineering Thermophysics
  
  
• Numerical Algebra and Scientific Computing
  
  
• Journal of Physics Through Computation
  
  
• Transactions on Particle and Nuclear Physics
  
  
• Multibody Systems, Nonlinear Dynamics and Control
  
  
• Complex Analysis and Geometry
  
  
• Dynamical Systems and Differential Equations
  
  
• Acoustics, Optics and Radio Physics
  
  
• Progress in Atomic and Molecular Physics
  
  
• Transactions on Condensed Matter Physics
  
  
• Transactions on Computational and Applied Mathematics
  
  
• Progress in Plasma Physics
  
  
• Combinatorics and Graph Theory
  
  
• Research and Practice of Mathematics & Statistics
  
  
• Nuclear Techniques and Applications
  
  
• Journal of Photonics Research
  
  
• Journal of Compressors and Refrigeration
  
  
• Journal of Theoretical Physics Frontiers
  
  
• Journal of Nonlinear Science and Complexity
  
  
• Vacuum Science Journal
  
  
• Computational Fluid Dynamics