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.

Dynamics of some Environmentally Significant Pesticides in a Tropical Waterway - A Toxicological Approach

Industrial pollutants, consisting of heavy metals, petroleum residues, petrochemicals, and a wide spectrum of pesticides, enter the marine environment on a massive scale and pose a very serious threat to all forms of aquatic life. Although, earlier, efforts were directed towards the identification of pollutants and their major sources, because of a growing apprehension about the potential harm that pesticides can inflict upon various aquatic fauna and flora, research on fundamental and applied aspects of pesticides in the aquatic environment has mushroomed to a point where it has become difficult to even keep track of the current advances and developments. The Cochin Estuarine System (CES), adjoining the Greater Cochin area, receives considerable amounts of domestic sewage, urban wastes, agricultural runoff as well as effluent from the industrial units spread all along its shores. Since preliminary investigations revealed that the most prominent of organic pollutants discharged to these estuarine waters were the pesticides, the present study was designed to analyse the temporal and spatial distribution profile of some of the more toxic, persistent pesticides ——— organochlorines such as DDT and their metabolites; HCH-isomers; a cyclodiene compound," Endosulfan and a widely distributed, easily degradable, organophosphorus compound, Malathion, besides investigating their sorptional and toxicological characteristics. Although, there were indications of widespread contamination of various regions of the CBS with DDT, HCH-isomers etc., due to inadequacies of the monitoring programmes and due to a glaring void of baseline data the causative factors could not identified authentically. Therefore, seasonal and spatial distributions of some of the more commonly used pesticides in the CES were monitored systematically, (employing Gas Chromatographic techniques) and the results are analysed.

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.

Theoretical approach to the magnetostructural correlations in spin-Peierls compound CuGeO3

A theoretical density-functional study has been carried out to analyze the exchange coupling in the chains of CuGeO3 using discrete models. The results show a good agreement with the experimental exchange coupling constant (J) together with a strong dependence of J with the Cu-O-Cu angle. The calculation of the J values for a distorted model indicates a larger degree of dimerization than those reported previously.

Some characterization problems associated with the bivariate exponential and geometric distributions

It is highly desirable that any multivariate distribution possessescharacteristic properties that are generalisation in some sense of the corresponding results in the univariate case. Therefore it is of interest to examine whether a multivariate distribution can admit such characterizations. In the exponential context, the question to be answered is, in what meaning— ful way can one extend the unique properties in the univariate case in a bivariate set up? Since the lack of memory property is the best studied and most useful property of the exponential law, our first endeavour in the present thesis, is to suitably extend this property and its equivalent forms so as to characterize the Gumbel's bivariate exponential distribution. Though there are many forms of bivariate exponential distributions, a matching interest has not been shown in developing corresponding discrete versions in the form of bivariate geometric distributions. Accordingly, attempt is also made to introduce the geometric version of the Gumbel distribution and examine several of its characteristic properties. A major area where exponential models are successfully applied being reliability theory, we also look into the role of these bivariate laws in that context. The present thesis is organised into five Chapters

An inhibitory compound produced by Pseudomonas with effectiveness on Vibrio harveyi

Persistence of the antivibrio property of the potential antagonistic probiotics, Pseudomonas MCCB 102 and 103, at di¡erent temperatures, pH and in organic solvents was studied. The antivibrio compound was extracted, puri¢ed and characterized using thin-layer chromatography, high-pressure liquid chromatography, liquid chromatography-mass spectroscopy, UV^ Vis and nuclear magnetic resonance spectroscopy and identi¢ed as N-methyl-1-hydroxyphenazine, a phenazine antibiotic. The toxicity of the compound was tested in Penaeus monodon haemocyte culture and the IC50 valuewas found to be1.4 0.31mg L 1. The compound was found to be bacteriostatic at 0.5mg L 1. Its stability to varying temperature, pH, organic solvents, prolonged shelf-life and vibriostatic nature point to its suitability for prophylatic aquaculture application.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables