IJPAM: Volume 76, No. 4 (2012)

AN UNORTHODOX PARAMETRIC MEASURES
OF INFORMATION AND CORRESPONDING
MEASURES OF FUZZY INFORMATION

Rohit Kumar Verma$^1$, C.L. Dewangan$^2$, P. Jha$^3$
$^1$Department of Mathematics
Bhilai Institute of Technology
Durg (C.G.), INDIA
$^{2,3}$Department of Mathematics
Y.J. Government Chhattisgarh College
Raipur (C.G.), INDIA


Abstract. A new parametric function

\begin{displaymath} V_{a}\left( P \right)=\sum\limits_{i=1}^n \ln {\left( 1+ap_{... ...\limits_{i=1}^n \ln {p_{i}-\ln \left( 1+a \right)} },\quad a>0 \end{displaymath}

is proposed for the probability distribution, $P=\left( p_{1},p_{2},\mathellipsis \mathellipsis \mathellipsis ,p_{n} \right)$ and its properties are studied. In this paper all functions are twice differentiable and are used to obtain the related measure of directed divergence, logistic type growth models and its measurement in fuzzy set. We also investigate the monotonic character of the proposed function and its corresponding multivariate normal distribution.

Received: February 14, 2012

AMS Subject Classification:

Key Words and Phrases: measure of entropy, directed divergence, multivariate normal distribution, logistic type growth model, innovation model, information theory

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 4