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

New High Permittivity and Low Loss Ceramics in the Bao-Ti02- Nb205 Composition

New dielectric ceramics with formula BaTi3Nb4, O„ and Ba6Til4Nbz039 have been prepared and characterized. BaTi3Nba017 was densified to 92% of TD after firing at 1310 oC for 4 h. However, Ba6Ti 1 4Nb2O39 fired under optimized conditions (1260 ` C for 4 h) showed only 85% TD together with secondary phase. The crystal system of both of the compositions is orthorhombic

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.

Seasonal ramification in the biochemical composition of organic matter in Chalakudy river-estuary

The present study which is the first of its kind in this region is an attempt to generate adequate information on the relative abundances, the seasonal and spatial variations as well as on the source and fate of organic compounds found associated with the dissolved, particulate and sedimentary compartments of Chalakudy river system. The study aimed at investigating variations, the relative proportion of dissolved, particulate and sedimentary fractions of these materials as well as the pollution extent so as to be able to comment on the present condition of this river-estuarine system. This thesis focuses attention on the role of biogeoorganics in modifying the ecological and environmental condition of the dissolved, particuIate and sediment compartments with their minute variability subjected to various physical, chemical and biogeochemical processes. A scheme of study encompassing all these objectives provides the frame work for the present investigation.

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.

Texture, composition and provinance of innershelf sediments between Narakkal and Purakkad, Kerala with special reference to the formation of Mud Banks

The continental shelf of southwest coast of India (Kerala) is broader and . flatter compared to that of the east coast. The unique characteristic feature of the study area (innershelf between Narakkal and Purakkad) is the intermittent appearance of 'mud banks' at certain locations during southwest monsoon. The strong seasonality manifests significant changes in the wind, waves, currents, rainfall, drainage etc., along this area. Peculiar geomorphological variation with high, mid and lowlands in the narrow strip of the hinterland, the geological formations mainly consisting of rocks of metamorphic origin and the humid tropical weathering conditions play significant role in regulating the shelf sedimentation. A complementary pattern of distri bution is observed for clay that shows an abundance in the nearshore. Silt, to a major extent, depicts semblance with clay distribution . Summation of the total asymmetry of grain size distribution are inferred from the variation of skewness and kurtosis.Factor I implies a low energy regime where the transportation and deposition phases are controlled mostly by pelagic suspension process as the factor loadings are dominant on finer phi sizes. The second Factor is inferred to be the result of a high energy regime which gives higher loadings on coarser size fractions. The third Factor which might be a transition phase (medium energy regime) representing the resultant flux of coastal circulation of the re-suspension/deposition and an onshoreoffshore advection by reworking and co-deposition of relict and modern sediments. The spatial variations of the energy regime based on the three end-member factor model exhibits high energy zone in the seaward portion transcending to a low energy one towards the coast.From the combined analysis of granulometry and SEM studies, it is concluded that the sandy patches beyond 20 m depth are of relict nature. They are the resultant responses of beach activity during the lower stand of sea level in the Holocene. Re-crystallisation features on the quartz grains indicate that they were exposed to subaerial weathering process subsequent to thei r deposition

Studies on the Composition and Structure of Palm Oil Glycerides

During the last couple of decades, the oil palm has emerged as the second largest source of edible oil in the world. Recently oil palm has been introduced commercially in India to augment edible oil supply in the country. Currently, about 10,000 hectares are under oil palm cultivation in India, and it is envisaged to cover about 6 lakh hectares in the coming years. Though oil palm is a major commercial oil crop, not much basic information on the lipids of the fruit (the source of palm oil) is available even where oil palm is cultivated in a very large scale. Being a new crop to India, it is of paramount importance to understand the basic chemistry/biochemistry of the lipids, which in turn, may find practical applications in the area of processing and product development. The present investigation entitled "Studies on the Composition and Structure of Palm Oil Glycerides" was designed with a view to elucidate the lipid composition and structure under conditions such as fruit development and processing.

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.

Studies on the effect of steriod hormones on the gronth and biochemical composition of the mullet liza.parsia (hamilton)

The present study has helped in finding out an efficient growth promoting substance for the fry of Liza garsia. 1Zfimethyltestosterone at the dosages of 2 mg/kg diet is the most effective anabolic agent for Liza parsia. The study also shows that by incorporating 8 mg MT/kg of diet the protein level in the diet could be reduced from 35 to 30%. thereby a significant saving in the cost of feed could be obtained. Further, the anabolic effect of MT helps to reduce the rearing period during the production of fingerlings from the fry stage.

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