Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

STUDIES ON TAXONOMY, DISTRIBUTION, ECOLOGY AND REPRODUCTIVE POTENTIAL OF ROTIFERS FROM SELECTED CENTRES IN COCHIN BACKWATER SYSTEM, KERALA

The studies were conducted in nine stations with varying ecological characteristics along Cochin backwaters and adjoining canals. Many workers opined that the distribution of rotifers is cosmopolitan. The significance of rotifers as first food for early larvae was indicated by Fujita. Aquaculture is a fast growing field in fisheries sector and it is gaining more importance as the fish landings and supply are getting irregular. A consistent supply of fish/shellfish can only be achieved through aquaculture. The success of any culture activity depends on the timely production of seeds of finfishes/shellfishes. The availability of wild seed is seasonal and erratic. So, a dependable source of seed of fishes and shellfishes is possible only through large scale production in hatchery. A successful seed production activity depends on the availability of a variety of suitable live feed organisms in sufficient quantities at the proper time for use in the larval stages. As the live feeds promote high growth rates, easy digestion, assimilation and the quality of not contaminating the culture water when compared to other artificial feeds, make the culture of live feed organisms the principal means of providing food for the larvae of finfishes and shellfishes. Rotifers are considered to be an excellent and indispensable food for larvae of many finfishes and crustaceans. It (1960) was the first to culture Brachionus plicatilis for feeding marine fish larvae, and now it is being extensively used as live feed in hatcheries all over the world. They are a group of microscopic organisms coming under the Phylum Rotifera which comprises of about 2000 species. Their slow swimming habits, ability to tolerate a wide range of salinities, parthenogenetic mode of reproduction and ability to get enriched easily, make rotifers an ideal live feed organism. The major factors such as temperature, salinity and food that influence the reproductive potential and thereby the population size of rotifer, Salinity is one of the most important aspect influencing the reproductive rate of rotifers. The feed type and feed concentration play a vital role in influencing the reproductive rate of rotifers. For culture of rotifers, the commonly used micro algae belong to Chlorella, Nannochloropsis, Isochrysis and Tetraselmis. While some studies have suggested that, algal diet has little effect on reproductive rates in 1979 while using the rotifer, Brachionus plicatilis as feed for the larvae of red sea bream, Pagrus major. It is generally accepted that rotifers play a pivotal role in the successful rearing of marine fish larvae.

Study on tropical rain with special reference to rain Drop Size Distribution and integral rain parameters using ground-based and satellite measurements

Department of Physics, Cochin University of Science and Technology

Bayesian Inference in Exponential and Pareto populations in the presence of Outliers

This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.

Parasite distribution and histopathological studies on certain commercially important fishes of cochin area

In order to check the damage caused by the parasites, even though it is difficult in open waters, a proper understanding of the seasonal variation in the distribution of the parasite and other factors like age of the host, sex of the host, which affect distribution of parasite is a must. Although several workers have carried out investigations on the taxonomy of metazoan parasites of marine and brackish water Fishes of India, very little attempt is made to correlate such investigations with the host and the environment. In this thesis such an attempt is made by the researcher. In chapter one the literature related to the prevalence, mean intensity of infection, and histopathological changes caused by the metazoan parasites, in particular by helminths, copepods and isopods, was reviewed. Chapter two contains observations on the distribution pattern of parasites in relation to the season, sex, and size of the host. It was found that the prevalence rate of radiorynchus_indicus infecting the alimentary canal of Tachysurugs mgacuglatus, Ergasilus sp. infecting the gills of T maculatus, and Lernaeeniicus ramosus found on the body surface of Qeimgipteirfugs jagonicus was higher during monsoon season. But agarna malayi found in the opercular chamber and Ehilometra cephalus infecting the gonads of valamugil speiglari showed a higher prevalence rate during the postmonsoon season. This was discussed on the basis of the hydrographical characteristics prevailing in the study area during the three different seasons. It was also observed that the sex of the host did not influence significantly the distribution pattern of the parasites. The reasons for this were also discussed. Invariably, the size of the host was found to influence the parasite distribution pattern. It was observed that the prevalence rate showed an increase with increase in size of the fish. This was discussed on the basis of food habits of the host, along with other aspects An attempt was made in chapter three to study the histopathological effects of‘ the various parasites on their respective sites of attachments on host Fishes. It was found that except Rhadinorhyhchugs indicus, all other parasites produced damages of varying intensity, in the form of hypertrophy, rhyperplasia, haemorrhage, tissue disruption and ulcers. Interestingly, E. indicus, an acantho— cephalid with a powerful proboscis for attachment was found not to cause any serious damage to the intestine of the host Fish. All these aspects are included in the third and final chapter of the thesis.

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

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

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

Quantile based entropy function

Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran, 2009). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions

Quantile based entropy function in past lifetime

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

Reliability Estimation of Open Source Software based Computational Systems

Software systems are progressively being deployed in many facets of human life. The implication of the failure of such systems, has an assorted impact on its customers. The fundamental aspect that supports a software system, is focus on quality. Reliability describes the ability of the system to function under specified environment for a specified period of time and is used to objectively measure the quality. Evaluation of reliability of a computing system involves computation of hardware and software reliability. Most of the earlier works were given focus on software reliability with no consideration for hardware parts or vice versa. However, a complete estimation of reliability of a computing system requires these two elements to be considered together, and thus demands a combined approach. The present work focuses on this and presents a model for evaluating the reliability of a computing system. The method involves identifying the failure data for hardware components, software components and building a model based on it, to predict the reliability. To develop such a model, focus is given to the systems based on Open Source Software, since there is an increasing trend towards its use and only a few studies were reported on the modeling and measurement of the reliability of such products. The present work includes a thorough study on the role of Free and Open Source Software, evaluation of reliability growth models, and is trying to present an integrated model for the prediction of reliability of a computational system. The developed model has been compared with existing models and its usefulness of is being discussed.