1,244 research outputs found
Entropy-Based Financial Asset Pricing
We investigate entropy as a financial risk measure. Entropy explains the
equity premium of securities and portfolios in a simpler way and, at the same
time, with higher explanatory power than the beta parameter of the capital
asset pricing model. For asset pricing we define the continuous entropy as an
alternative measure of risk. Our results show that entropy decreases in the
function of the number of securities involved in a portfolio in a similar way
to the standard deviation, and that efficient portfolios are situated on a
hyperbola in the expected return - entropy system. For empirical investigation
we use daily returns of 150 randomly selected securities for a period of 27
years. Our regression results show that entropy has a higher explanatory power
for the expected return than the capital asset pricing model beta. Furthermore
we show the time varying behaviour of the beta along with entropy.Comment: 21 pages, 6 figures, 3 tables and 4 supporting file
Application of Generalized Partial Volume Estimation for Mutual Information based Registration of High Resolution SAR and Optical Imagery
Mutual information (MI) has proven its effectiveness for automated multimodal image registration for numerous remote sensing applications like image fusion. We analyze MI performance with respect to joint histogram bin size and the employed joint histogramming technique. The affect of generalized partial volume estimation (GPVE) utilizing B-spline kernels with different histogram bin sizes on MI performance has been thoroughly explored for registration of high resolution SAR (TerraSAR-X) and optical (IKONOS-2) satellite images. Our experiments highlight possibility of an inconsistent MI behavior with different joint histogram bin size which gets reduced with an increase in order of B-spline kernel employed in GPVE. In general, bin size reduction and/or increasing B-spline order have a smoothing affect on MI surfaces and even the lowest order B-spline with a suitable histogram bin size can achieve same pixel level accuracy as achieved by the higher order kernels more consistently
Another Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we introduce a bivariate extensions of the new family. We discuss the dierent method of estimation of the model parameters and illustrate the potentiality of the family by means of two applications to real data. A brief simulation for evaluating Maximum likelihood estimator is done
Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented
Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework
The concept of positional information is central to our understanding of how
cells in a multicellular structure determine their developmental fates.
Nevertheless, positional information has neither been defined mathematically
nor quantified in a principled way. Here we provide an information-theoretic
definition in the context of developmental gene expression patterns and examine
which features of expression patterns increase or decrease positional
information. We connect positional information with the concept of positional
error and develop tools to directly measure information and error from
experimental data. We illustrate our framework for the case of gap gene
expression patterns in the early Drosophila embryo and show how information
that is distributed among only four genes is sufficient to determine
developmental fates with single cell resolution. Our approach can be
generalized to a variety of different model systems; procedures and examples
are discussed in detail
Estimating differential entropy using recursive copula splitting
A method for estimating the Shannon differential entropy of multidimensional
random variables using independent samples is described. The method is based on
decomposing the distribution into a product of the marginal distributions and
the joint dependency, also known as the copula. The entropy of marginals is
estimated using one-dimensional methods. The entropy of the copula, which
always has a compact support, is estimated recursively by splitting the data
along statistically dependent dimensions. Numerical examples demonstrate that
the method is accurate for distributions with compact and non-compact supports,
which is imperative when the support is not known or of mixed type (in
different dimensions). At high dimensions (larger than 20), our method is not
only more accurate, but also significantly more efficient than existing
approaches
Reliability analysis of the new exponential inverted topp–leone distribution with applications
The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress– strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed
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