Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution

Parameter Estimation in Minification Processes

In this article it is proved that the stationary Markov sequences generated by minification models are ergodic and uniformly mixing. These results are used to establish the optimal properties of estimators for the parameters in the model. The problem of estimating the parameters in the exponential minification model is discussed in detail.

Analysis of Some Queueing Models Related To N-Policy: Operations Research

This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Investigations on the Distribution Characteristics of Heavy Metals in Squid (Loligo spp.) in Relation to Levels in Food Fishes from the West Coast of India with a Perspective on Seafood Safety

The present study entitled "Investigations on the Distribution Characteristics of Heavy Metals in Squid (Loligo spp.) in Relation to Levels in Food Fishes from the West Coast of India with a Perspective on Seafood Safety"attempts to establish the base line data on metal levels in squids along the west coast of India. The study is of great relevance in the present context when utmost importance is being given for producing wholesome seafoods especially in the export market with a perspective on seafood safety.The thesis presents a comprehensive account of the base line data on important heavy metals, viz., Hg, Cd, Pb, Cu, Zn, Fe, Mn Cr and Ni in the edible and non-edible body components of the most abundant Loligo species, viz., L. duvauceli caught along the west coast of India.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Targeted Public Distribution System in Food Grains:Extent of Utlization by the Tribal Population in Kerala

In India, Food Security meant supply of food grains and the medium was Public Distribution System. Public Distribution System (PDS) is a rationing mechanism that entitles households to specified quantities of selected commodities at subsidized prices. The Objectives of PDS are maintaining Price Stability, rationing during times of scarcity, welfare of the poor, and keeping a check on private trade. Kerala has registered remarkable improvement in poverty reduction in general over the years among all social sections, including scheduled caste and scheduled tribe population. As part of the structural adjustment intended to reduce public expenditure, PDS has been modified as Revamped PDS (RPDS) during 1992 and later on as Targeted PDS (TPDS) in 1997, intended to target households on the basis of income criterion, classifying people as Below Poverty Line (BPL) and Above Poverty Line (APL). TPDS provides 25Kg. of food gra.ins through the Fair Price Shops per month @ Rs.3/- per Kg. of rice/ wheat to the BPL category and @Rs.8.90 and Rs.6.7O for rice and wheat respectively to the APL category of people. Since TPDS is intended to target the poor people, the subsidy spent by the government for the scheme should be beneficial to the poor people and naturally they should utilize the benefits by purchasing the food grains allotted under the scheme. Several studies have shown that there is underutilization of the allotments under TPDS. Therefore, the extent of utilization of TPDS in food grains, how and why remains as a major hurdle, in improving the structure and system of PDS. Livelihood of the tribal population being under threat due to increasing degradation of the resources, the targeting system ought to be effective among the tribal population. Therefore, performance of the TPDS in food grains, in terms of the utilization by the tribal population in Kerala, impact thereof and the factors, if any, affecting proper utilization were considered as the research problem in this study. The study concentrated on the pattern of consumption of food grains by the tribal people, whether their hunger needs are met by distribution of food grains through the TPDS, extent to which TPDS in food grains reduce their share of expenditure on food in the total household expenditure, and the factors affecting the utilization of the TPDS in food grains by the tribal population. Going through the literature, it has been noted that only few studies concentrated on the utilization of TPDS in food grains among the tribal population in Kerala.The Research Design used in this study is descriptive in nature, but exploratory in some aspects. Idukki, Palakkad and Wayanad have more than 60% of the population of the tribals in the state. Within the three districts mentioned above, 14 villages with scheduled tribe concentration were selected for the study. 95 tribal colonies were selected from among the various tribal settlements. Collection of primary data was made from 1231 households with in the above tribal colonies. Analysis of data on the socio-economic factors of the tribal people, pattern of food consumption, extent of reduction in the share of expenditure on food among the household expenditure of the tribal people and the impact of TPDS on the tribal families etc. and testing of hypotheses to find out the relation/association of each of the six variables, using the data on BPL and APL categories of households separately have resulted in findings such as six percent of the tribal families do not have Ration Cards, average per capita consumption of food grains by the tribal people utilizing TPDS meets 62% of their minimum requirement, whereas the per capita consumption of food grains by the tribal people is higher than the national average per capita consumption, 63% deficiency in food grains may be felt by tribal people in general, if TPDS is withdrawn, and the deficit for BPL tribal people may be 82%, TPDS facilitates a reduction of 9.71% in the food expenditure among the total household expenditure of the tribal people in general, share of food to non-food among BPL category of tribals is 55:45 and 40:60 among the APL, Variables, viz. household income, number of members in the family and distance of FPS from tribal settlements etc. have influence on the quantity of rice being purchased by the tribal people from the Fair Price Shops, and there is influence of household income and distance of FPS from tribal settlements on the quantity of rice being purchased by the tribal people from the open market. Rationing with differential pricing on phased allotments, rectification of errors in targeting, anomalies in norms and procedures for classifying tribal people as BPL/APL, exclusive Income Generation for tribal population, paddy cultivation in the landholdings possessed by the tribal people, special drive for allotment of Ration Cards to the tribal people, especially those belonging to the BPL category, Mobile Fair Price Shops in tribal settlements, ensure quality of the food grains distributed through the TPDS, distribution of wheat flour in packed condition instead of wheat through the Fair Price Shops are recommended to address the shortcomings and weaknesses of the TPDS vis-avis the tribal population in Kerala.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

Survey of coral lagoons of Laksbadweep Atolls using line intercept transect (LIT) technique

The present study aims at surveying the coral lagoons of four islands viz. Kavarathi, Kalpeni, Kadmat and Agathi, which include quantitative survey of the major benthic forms using Line Intercept Transect (LIT) technique and hydrographical study of these lagoon waters The distribution of PHC in the lagoons has also been followed to understand, the effects of introduction of flat bottomed ferry boats to the islands.From a biological monitoring stand point for the assessment of manmade disturbance of the coral reefs, it IS highly essential to identify faunal assemblages which will contain 'flag-stones' specIes as indicators of such disturbances. Among the known faunal assemblages In coral reefs the most diverse groups of sensitive species belongs to bryozoan assemblage. Therefore, the most common species of bryozoans distributed along the atolls and reef flats were collected and described in this work Along with this, bryozoans associated with coral from other parts of Indian ocean have also been added so as to provide a comprehensive picture of the distribution of bryozoans in the coral reefs.

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.

Computational models for the prediction of severe thunderstorms over east indian region

Thunderstorm is one of the most spectacular weather phenomena in the atmosphere. Many parts over the Indian region experience thunderstorms at higher frequency during pre-monsoon months (March- May), when the atmosphere is highly unstable because of high temperatures prevailing at lower levels. Most dominant feature of the weather during the pre-monsoon season over the eastern Indo-Gangetic plain and northeast India is the outburst of severe local convective storms, commonly known as ‘Nor’wester’ or ‘Kalbaishakhi’. The severe thunderstorms associated with thunder, squall line, lightning and hail cause extensive losses in agriculture, damage to structure and also loss of life. The casualty due to lightning associated with thunderstorms in this region is the highest in the world. The highest numbers of aviation hazards are reported during occurrence of these thunderstorms. In India, 72% of tornadoes are associated with this thunderstorm.

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Establishment and characterization of India's first marine fish cell line (SISK) from the kidney of sea bass (Lates calcarifer)

A continuous cell line (SISK) from kidney of sea bass, Lates calcarifer, has been established and characterized. The cell line was maintained in Leibovitz' L-15 supplemented with 15% fetal bovine serum. This cell line has been subcultured more than 100 times over a period of 2 years. The SISK cell line consists of predominantly of epithelial-like cells. These cells showed strong positive for epithelial markers such as cytokeratin 19 and pancytokeratin. The cells were able to grow at temperature between 25 and 32 °C with optimum temperature of 28 °C. The growth rate of sea bass kidney cells increased as the FBS proportion increased from 2% to 20% at 28 °C with optimum growth at the concentrations of 15% or 20% FBS. The distribution of chromosome number was 30 to 56 with a modal peak at 48 chromosomes. Polymerase chain reaction products were obtained from SISK cells and tissues of sea bass with primer sets of microsatellite markers of sea bass. Five fish viruses were tested on this cell line to determine its susceptibility to these viruses and this was found to be susceptible to MABV NC1 and nodavirus, and the infection was confirmed by RT-PCR and CPE. This suggests that the SISK cell line has good potential for the isolation of various fish viruses. This cell line has been shown to be susceptible to bacterial extracellular products. The SISK cell line is the India's first marine fish cell line.

Some Dynamic Generalized Information Measures In The Context Of Weighted Models

In this paper, we study some dynamic generalized information measures between a true distribution and an observed (weighted) distribution, useful in life length studies. Further, some bounds and inequalities related to these measures are also studied