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On the functional relationship between entropy and variance with related applications |
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| Authors: | Debabrata Mukher jee Makarand V Ratnaparkhi |
| Institution: | Dept of Statistics and Computer Systems , Lorex Pharmaceutical Co , Skokie, Illinois |
| Abstract: | The functional relationship between entropy and variance is investigated for some well-known distributions. The distributions considered here are the reparameterized versions of the original forms. Such a reparameterization is necessary as in each case we have a common variance. The related graphs of entropy as a function of variance are used for certain comparisons. Further, within the class of distributions having a common variance, a measure of affinity between these distributions is proposed using entropy. A few aspects of the sampling distributions of an estimator of entropy, when the samples are either from the normal or from the exponential distributions, are discussed with a view to possible applications in the testing of hypotheses for related parameters |
| Keywords: | Entropy variance affini ty measure normal Laplace logistics t type 1 extreme-value generalized gamma generalized norma gamma exponential Wei bull uniform Pare to triangular binomial Poisson negative binomial geometric distributions |