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.

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

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space

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

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Influence of Processing Variables on Protein Quality and Frozen Storage Stability of Two Commercially Important Species of Squid (Loligo duvaucelii and Doryteuthis sibogae )

Cephalopods are utilized as an important food item in various countries because of its delicacy as raw consumed food. Mainly sepia and loligo are consumed raw by Japanese and Russians. The freshness of the products is very important when the product is consumed raw. The major species that dominate our squid catch are Loligo duvaucelii and Doryteuthis sibogae. There is a noticeable difference in the quality of both the species. The needle squid (Doryteuthis sibogae ) contributes about 35% of the total squid landing. Due to the fast deterioration , a major portion of the needle squid, which is caught during the first few hauls, is thrown back to sea. The catch in the last hauls only are taken to the landing centers. At present the needle squid is processed as blanched rings and the desired quality is not obtained if it is processed as whole, whole cleaned or as tubes. In this study an attempt is made to investigate the biochemical characteristics in both the species of squid in relation to their quality and, the process control measures to be adopted. The effect of various treatments on their quality and the changes in proteolytic and lysosomal enzymes under various processing conditions are also studied in detail.Thus this study can provide the seafood industry with relevant suggestions and solutions for effective utilization of both the species of squid with emphasis on needle squid.

Data Security in Fault Tolerant Hard Real Time Systems- Use of Time Dependant Multiple Random Cipher Code

The present research problem is to study the existing encryption methods and to develop a new technique which is performance wise superior to other existing techniques and at the same time can be very well incorporated in the communication channels of Fault Tolerant Hard Real time systems along with existing Error Checking / Error Correcting codes, so that the intention of eaves dropping can be defeated. There are many encryption methods available now. Each method has got it's own merits and demerits. Similarly, many crypt analysis techniques which adversaries use are also available.

Career Advancement of MBAs: A study on the effect of personal, professional,organisational and environmental variables

School of Management Studies, Cochin University of Science and Technology

Studies on the universal parameters and onset of chaos in dissipative systems

It has become clear over the last few years that many deterministic dynamical systems described by simple but nonlinear equations with only a few variables can behave in an irregular or random fashion. This phenomenon, commonly called deterministic chaos, is essentially due to the fact that we cannot deal with infinitely precise numbers. In these systems trajectories emerging from nearby initial conditions diverge exponentially as time evolves)and therefore)any small error in the initial measurement spreads with time considerably, leading to unpredictable and chaotic behaviour The thesis work is mainly centered on the asymptotic behaviour of nonlinear and nonintegrable dissipative dynamical systems. It is found that completely deterministic nonlinear differential equations describing such systems can exhibit random or chaotic behaviour. Theoretical studies on this chaotic behaviour can enhance our understanding of various phenomena such as turbulence, nonlinear electronic circuits, erratic behaviour of heart and brain, fundamental molecular reactions involving DNA, meteorological phenomena, fluctuations in the cost of materials and so on. Chaos is studied mainly under two different approaches - the nature of the onset of chaos and the statistical description of the chaotic state.

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

Influence of compounding and process variables on quality of condams made from natural rubber latex

Condoms are widely accepted as a contraceptive for family planning and population control. It is also accepted as the most effective barrier against sexually transmitted diseases, especially AIDS, the incurable disease. But presence of pinholes and low film strength of condoms make it unsuitable for the purpose. Quality improvement of condoms by reducing the pinhole formation and increasing the film strength is thus an essential requirement for population control as well as for preventing the spread of sexually transmitted diseases. Strict implementation of WHO specification of condoms further increases the rejection percentage. This causes higher rejection loss to condom manufacturers because the defects could be identified only at the final stage of processing. If the influence of various factors which cause these defects is known, manufacturers can take remedial measures to reduce the defectives so that rejection loss can be decreased and quality of condoms increased. In the present study, it was proposed to conduct experiments to improve the quality of condoms by reducing the pinhole rejection percentage and increasing the tensile properties, burst volume, and burst pressure. Ageing property improvement also was an important target among other parameters. Until a cure for AIDS is found, a high quality latex condom is the only effective device in the prevention of the spread of HIV, AIDS and STD's. Hence it is all the more necessary to have high quality condoms.