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.

A Bivariate Pareto Distribution with Freund’s Dependence Structure

Department of Statistics, Cochin University of Science and Technology

On Finite Mixture of Pareto and Beta Distnbutions

Department of Statistics, 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.

On Truncated Versions of Certain Measures of Inequality and Stability

The present study focuses attention on defining certain measures of income inequality for the truncated distributions and characterization of probability distributions using the functional form of these measures, extension of some measures of inequality and stability to higher dimensions, characterization of bivariate models using the above concepts and estimation of some measures of inequality using the Bayesian techniques. The thesis defines certain measures of income inequality for the truncated distributions and studies the effect of truncation upon these measures. An important measure used in Reliability theory, to measure the stability of the component is the residual entropy function. This concept can advantageously used as a measure of inequality of truncated distributions. The geometric mean comes up as handy tool in the measurement of income inequality. The geometric vitality function being the geometric mean of the truncated random variable can be advantageously utilized to measure inequality of the truncated distributions. The study includes problem of estimation of the Lorenz curve, Gini-index and variance of logarithms for the Pareto distribution using Bayesian techniques.

Antibody Based Diagnostic for Detection Of Vibrios and their Biological Control using Antagonistic Bacteria in Macrobrachium Rosenbergii Larval Rearing Systems

The main objective of the work undertaken here was to develop an appropriate microbial technology to protect the larvae of M.rosenbergii in hatchery from vibriosis. This technology precisely is consisted of a rapid detection system of vibrios and effective antagonistic probiotics for the management of vibrios. The present work was undertaken with the realizations that to stabilize the production process of commercial hatcheries an appropriate, comprehensive and fool proof technology is required primarily for the rapid detection of Vibrio and subsequently for its management. Nine species of Vibrio have been found to be associated with larvae of M. rosenbergii in hatchery. Haemolytic assay of the Vibrio and Aeromonas on prawn blood agar showed that all isolates of V. alginolyticus and Aeromonas sp., from moribund, necrotized larve were haemolytic and the isolates of V.cholerae, V.splendidus II, V.proteolyticus and V.fluvialis from the larvae obtained from apparently healthy larval rearing systems were non-haemolytic. Hydrolytic enzymes such as lipase, chitinase and gelatinase were widespread amongst the Vibrio and Aeromonas isolates. Dominance of V.alginolyticus among the isolates from necrotic larvae and the failure in isolating them from rearing water strongly suggest that they infect larvae and multiply in the larval body and cause mortality in the hatchery. The observation suggested that the isolate V. alginolyticus was a pathogen to the larvae of M.rosenbergii. To sum up, through this work, nine species of Vibrio and genus Aeromonas associated with M.rosenbergii larval rearing systems could be isolated and segregated based on the haemolytic activity and the antibodies (PA bs) for use in diagnosis or epidemiological studies could be produced, based on a virulent culture of V.alginolyticus. This could possibly replace the conventional biochemical tests for identification. As prophylaxis to vibriosis, four isolates of Micrococcus spp. and an isolate of Pseudomonas sp. could be obtained which could possibly be used as antagonistic probiotics in the larval rearing system of M.rosenbergii.

Heterotrophic Bacteria Associated with Healthy and Moribund Larvae of Penaeus monodon H.Milne Edwards

Heterotrophic bacterial flora of Pmonadon from an apparently healthy hatchery system as well as a pool with heavy mortality were isolated and studied. In the healthy systems comparatively higher generic diversity with Pseudomonas, Acinetobacter, Bacillus, Micrococcus, members of the family Enterobacteriaceae and coryneform group in the diminishing order of dominance was recorded. Meanwhile from the moribund larvae and rearing water Aeromonas and Pseudomonas could be isolated in almost equal proportions. Strikingly, Aeromonas could not be isolated from the apparently healthy larval rearing system and its exclusive occurrence in the sick culture system in comparatively higher percentage suggested its possible role in the mortality. They were found to be highly halophilic exhibiting growth at 10% NaCl. On testing their sensitivity to twenty antibiotics, four of them (Streptomycin, Gentamycin, Methamine mandelate and Cloramphenicol) were found to be effective on all the isolates of Aeromonas and Pseudomonas suggesting their possible application in the hatchery system in times of emergency. While doing so, Streptomycin would do comparatively better than the others as the minimum inhibitory dose required was comparatively lower (200ppm) within a period of 24 hours

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

Estimation for the semipareto processes

This paper proposes different estimators for the parameters of SemiPareto and Pareto autoregressive minification processes The asymptotic properties of the estimators are established by showing that the SemiPareto process is α-mixing. Asymptotic variances of different moment and maximum likelihood estimators are compared.

A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

Contribution of size fractions of planktonic algae to primary organic productivity in the coastal waters of Cochin- south west coast of lndia

This thesis entitled “Contribution of size fractions of planktonic algae to primary organic productivity in the coastal waters of cochin,south west coast of india”. Marine ecosystems planktonic algae are the most important primary producers on wliich considerable attention is being given on account of their supreme status in the marine food chain.The study of primary production in the Indian Ocean started With DANA (I928-30),, John Murray t I933-34). Discovery ( I934) and Albatross (I947-48) expeditions which tried to evaluate productivity from nutrients and standing crop of phytoplankton .The bioproductivity of the marine environment is dependent on various primary producers. ranging in size from picoplankton to larger macro phytoplankton. The quantity and quality of various size fractions of planktonic algae at any locality depend mainly on the hydrographic conditions of the area .In the coastal waters of Cochin- south west coast of lndia. Planktonic algal community is composed mainly of the diatoms, the dinoflagellates, the blue-green algae and the silicoflagellates, the former two contributing the major flora and found distributed in the all size fractions. The maximum number of species of diatoms at station 1 and station 2 was found in the pre-monsoon season.. The size groups of planktonic algae greater than 53 um are dominated by filamentous- chain forming and colonial diatoms. The coastal waters of Cochin. planktonic algae less than 53 um in size contribute significantly to primary productivity and the biodiversity of the microflora, indicating the presence of rich fishery resources in the south west coast of india.The study of different size fractions of planktonic algae and their relative contribution to the primary organic production is a useful tool for the estimation of the quantity and quality of fisheries.A deeper investigation on the occurrence of these microalgae and proper identification of their species would be of immense help for the assessment of the specificity and magnitude of fishery resources.

Effect of industrial pollution on the benthic communities of a tropical estuary

Cochin backwaters, a tropical barbuilt estuary is well known for its prawn, molluscan and demersal fisheries. Also it formed the dumping area for sewage,235 retting of husks and discharge of effluents from industries located on either side of it. As a result the fishery is being gradually dwindled year after year due to the lowering of the water quality. The effect of industrial polution on the benthic community of this tropical estuary was worked out. An area extending over 21 km from the mouth of the estuary to upstream of industrial belt was selected. Temporal and spatial variations of 16 environmental parameters at 9 stations along the area were monitored monthly during 1981. Benthic fauna of these 9 stations consisted of amphipods , polychaetes, isopods, tanaidaceans, molluscs and other crustaceans (Decapods, Acetes, Alpheids, Balanus, insect larvae, chironomid larvae, cumacea and some fresh water forms ). Apart from these, sea anemone, flat worms, nematodes, sipunculoids, echinoderms and fishes were also encountered. 75 species belonging to 31 faunal groups were identified. Of these 31 groups, amphipods, polychaedes, isopods, tanaidaceans and molluscs were numerically abundant. Rest of the 26 groups (including 13 riverine forms) were found less significant due to their rare occurrence/low numerical abundance. Polychaetes and molluscs were the only major groups present at all the stations.

Multi-objective assembly job shop scheduling using genetic algorithm and tabu search

Assembly job shop scheduling problem (AJSP) is one of the most complicated combinatorial optimization problem that involves simultaneously scheduling the processing and assembly operations of complex structured products. The problem becomes even more complicated if a combination of two or more optimization criteria is considered. This thesis addresses an assembly job shop scheduling problem with multiple objectives. The objectives considered are to simultaneously minimizing makespan and total tardiness. In this thesis, two approaches viz., weighted approach and Pareto approach are used for solving the problem. However, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. Two metaheuristic techniques namely, genetic algorithm and tabu search are investigated in this thesis for solving the multiobjective assembly job shop scheduling problems. Three algorithms based on the two metaheuristic techniques for weighted approach and Pareto approach are proposed for the multi-objective assembly job shop scheduling problem (MOAJSP). A new pairing mechanism is developed for crossover operation in genetic algorithm which leads to improved solutions and faster convergence. The performances of the proposed algorithms are evaluated through a set of test problems and the results are reported. The results reveal that the proposed algorithms based on weighted approach are feasible and effective for solving MOAJSP instances according to the weight assigned to each objective criterion and the proposed algorithms based on Pareto approach are capable of producing a number of good Pareto optimal scheduling plans for MOAJSP instances.

Heterotrophic Bacteria Associated with Healthy and Moribund Larvae of Penaeus monodon H.Milne Edwards

Heterotrophic bacterial flora of Pmonadon from an apparently healthy hatchery system as well as a pool with heavy mortality were isolated and studied. In the healthy systems comparatively higher generic diversity with Pseudomonas, Acinetobacter, Bacillus, Micrococcus, members of the family Enterobacteriaceae and coryneform group in the diminishing order of dominance was recorded. Meanwhile from the moribund larvae and rearing water Aeromonas and Pseudomonas could be isolated in almost equal proportions. Strikingly, Aeromonas could not be isolated from the apparently healthy larval rearing system and its exclusive occurrence in the sick culture system in comparatively higher percentage suggested its possible role in the mortality. They were found to be highly halophilic exhibiting growth at 10% NaCl. On testing their sensitivity to twenty antibiotics, four of them (Streptomycin, Gentamycin, Methamine mandelate and Cloramphenicol) were found to be effective on all the isolates of Aeromonas and Pseudomonas suggesting their possible application in the hatchery system in times of emergency. While doing so, Streptomycin would do comparatively better than the others as the minimum inhibitory dose required was comparatively lower (200ppm) within a period of 24 hours