Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

A Microstrip Patch Resonator with a Via Connecting Ground Plane

patch resonator with a via connecting ground plane is proposed and studied experimentally. The resonant frequency of this patch resonator is tunable up to about 34 % by adjusting the via position in the center line. The lowest resonant frequency of this patch resonator has been reduced by more than 64% of the same size patch resonator

Axially Symmetric Radiation Patterns from Flanged E-Plane Sectoral Horn

A simple technique for obtaining identical E- and H-plane patterns from E-plane sectoral feed horn is presented. Halfpower beam width and gain of the antenna are also improved considerably. Experimental results for a number of horns with flanges of various parameters are also presented. This system may find practical application in radar and space communication systems

Bivariate semi-Pareto distributions and processes

A bivariate semi-Pareto distribution is introduced and characterized using geometric minimization. Autoregressive minification models for bivariate random vectors with bivariate semi-Pareto and bivariate Pareto distributions are also discussed. Multivariate generalizations of the distributions and the processes are briefly indicated.

Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Characterization of Probability Distributions by Variance Bounds and its Applications

Department of Statistics, Cochin University of Science and Technology

Some Properties of Weighted Distributions for Truncated Random Variables

The present study gave emphasis on characterizing continuous probability distributions and its weighted versions in univariate set up. Therefore a possible work in this direction is to study the properties of weighted distributions for truncated random variables in discrete set up. The problem of extending the measures into higher dimensions as well as its weighted versions is yet to be examined. As the present study focused attention to length-biased models, the problem of studying the properties of weighted models with various other weight functions and their functional relationships is yet to be examined.

Investigations on Broadband Plannar Monoplole Antennas with Truncated Ground Plane

The space constraints on wireless gadgets is a challenge to antenna designers as the ground plane dimensions of the printed monopole significantly affect s the antenna characteristics.Investigations on ground plane truncations have led to the development of an extremely broad band printed monopole antenna.Omnidirectional radiation characteristics with moderate gain makes this antenna highly suitable for mobile/wireless applications .This thesis also highlights the development of UWB printed antenna along with design equations .Optimum ground plane dimensions for compact antenna applications,folding technique for miniaturization and double folding for dual band application are the other highlights of this thesis.

Strip-loaded hollow dielectric H-plane sectoral horn antennas for square radiation pattern

The radiation characteristics of a new type of hollow dielectric H-plane sectoral horn antenna are presented. Metallic strips of optimum length are loaded on the H-walls of the sectoral horns. The effects of strip loading for producing square patterns in the H plane are discussed.

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Bivarite burr distributions

The present work is organized into six chapters. Bivariate extension of Burr system is the subject matter of Chapter II. The author proposes to introduce a general structure for the family in two dimensions and present some properties of such a system. Also in Chapter II some new distributions, which are bivariate extension of univariate distributions in Burr (1942) is presented.. In Chapter III, concentrates on characterization problems of different forms of bivariate Burr system. A detailed study of the distributional properties of each member of the Burr system has not been undertaken in literature. With this aim in mind in Chapter IV is discussed with two forms of bivariate Burr III distribution. In Chapter V the author Considers the type XII, type II and type IX distributions. Present work concludes with Chapter VI by pointing out the multivariate extension for Burr system. Also in this chapter the concept of multivariate reversed hazard rates as scalar and vector quantity is introduced.