6 research outputs found
Varentropy Decreases Under the Polar Transform
We consider the evolution of variance of entropy (varentropy) in the course
of a polar transform operation on binary data elements (BDEs). A BDE is a pair
consisting of a binary random variable and an arbitrary side
information random variable . The varentropy of is defined as the
variance of the random variable . A polar transform of
order two is a certain mapping that takes two independent BDEs and produces two
new BDEs that are correlated with each other. It is shown that the sum of the
varentropies at the output of the polar transform is less than or equal to the
sum of the varentropies at the input, with equality if and only if at least one
of the inputs has zero varentropy. This result is extended to polar transforms
of higher orders and it is shown that the varentropy decreases to zero
asymptotically when the BDEs at the input are independent and identially
distributed.Comment: Presented in part at ISIT 2014. Accepted for publication in the IEEE
Trans. Inform. Theory, March 201
Extropy and Varextropy estimators with applications
In many statistical studies, the measure of uncertainties like entropy,
extropy, varentropy and varextropy of a distribution function is of prime
interest. This paper proposes estimators of extropy and varextropy. Proposed
estimators are consistent. Based on extropy estimator, a test of symmetry is
given. The proposed test has the advantage that we do not need to estimate the
centre of symmetry. The critical value and power of the proposed test
statistics have been obtained. The test procedure has been implemented on six
real-life data sets to verify its performance in identifying the symmetric
nature.Comment: arXiv admin note: text overlap with arXiv:2209.0670
A NEW GENERALIZED VARENTROPY AND ITS PROPERTIES
The variance of Shannon information related to the random variable , which is called varentropy, is a measurement that indicates, how the information content of is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them
A New Generalized Varentropy and its Properties
The variance of Shannon information related to the random variable X, which is called varentropy, is a measurement that indicates, how the information content of X is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions that improved the quality of the paper