Concomitants of Order Statistics from Morgenstern Family

The study deals with the distribution theory and applications of concomitants from the Morgenstern family of bivariate distributions.The Morgenstern system of distributions include all cumulative distributions of the form FX,Y(X,Y)=FX(X) FY(Y)[1+α(1-FX(X))(1-FY(Y))], -1≤α≤1.The system provides a very general expression of a bivariate distributions from which members can be derived by substituting expressions of any desired set of marginal distributions.It is a brief description of the basic distribution theory and a quick review of the existing literature.The Morgenstern family considered in the present study provides a very general expression of a bivariate distribution from which several members can be derived by substituting expressions of any desired set of marginal distributions.Order statistics play a very important role in statistical theory and practice and accordingly a remarkably large body of literature has been devoted to its study.It helps to develop special methods of statistical inference,which are valid with respect to a broad class of distributions.The present study deals with the general distribution theory of Mk, [r: m] and Mk, [r: m] from the Morgenstern family of distributions and discuss some applications in inference, estimation of the parameter of the marginal variable Y in the Morgestern type uniform distributions.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

Studies on nitrifying microorganisms in Cochin Estuary and adjacent coastal waters

This thesis entitled “Studies on Nitrifying Microorganisms in Cochin Estuary and Adjacent Coastal Waters” reports for the first time the spatial andtemporal variations in the abundance and activity of nitrifiers (Ammonia oxidizingbacteria-AOB; Nitrite oxidizing bacteria- NOB and Ammonia oxidizing archaea-AOA) from the Cochin Estuary (CE), a monsoon driven, nutrient rich tropicalestuary along the southwest coast of India. To fulfil the above objectives, field observations were carried out for aperiod of one year (2011) in the CE. Surface (1 m below surface) and near-bottomwater samples were collected from four locations (stations 1 to 3 in estuary and 4 in coastal region), covering pre-monsoon, monsoon and post-monsoon seasons. Station 1 is a low saline station (salinity range 0-10) with high freshwater influx While stations 2 and 3 are intermediately saline stations (salinity ranges 10-25). Station 4 is located ~20 km away from station 3 with least influence of fresh water and is considered as high saline (salinity range 25- 35) station. Ambient physicochemical parameters like temperature, pH, salinity, dissolved oxygen (DO), Ammonium, nitrite, nitrate, phosphate and silicate of surface and bottom waters were measured using standard techniques. Abundance of Eubacteria, total Archaea and ammonia and nitrite oxidizing bacteria (AOB and NOB) were quantified using Fluorescent in situ Hybridization (FISH) with oligonucleotide probes labeled withCy3. Community structure of AOB and AOA was studied using PCR Denaturing Gradient Gel Electrophoresis (DGGE) technique. PCR products were cloned and sequenced to determine approximate phylogenetic affiliations. Nitrification rate in the water samples were analyzed using chemical NaClO3 (inhibitor of nitrite oxidation), and ATU (inhibitor of ammonium oxidation). Contribution of AOA and AOB in ammonia oxidation process was measured based on the recovered ammonia oxidation rate. The contribution of AOB and AOA were analyzed after inhibiting the activities of AOB and AOA separately using specific protein inhibitors. To understand the factors influencing or controlling nitrification, various statistical tools were used viz. Karl Pearson’s correlation (to find out the relationship between environmental parameters, bacterial abundance and activity), three-way ANOVA (to find out the significant variation between observations), Canonical Discriminant Analysis (CDA) (for the discrimination of stations based on observations), Multivariate statistics, Principal components analysis (PCA) and Step up multiple regression model (SMRM) (First order interaction effects were applied to determine the significantly contributing biological and environmental parameters to the numerical abundance of nitrifiers). In the CE, nitrification is modulated by the complex interplay between different nitrifiers and environmental variables which in turn is dictated by various hydrodynamic characteristics like fresh water discharge and seawater influx brought in by river water discharge and flushing. AOB in the CE are more adapted to varying environmental conditions compared to AOA though the diversity of AOA is higher than AOB. The abundance and seasonality of AOB and NOB is influenced by the concentration of ammonia in the water column. AOB are the major players in modulating ammonia oxidation process in the water column of CE. The distribution pattern and seasonality of AOB and NOB in the CE suggest that these organisms coexist, and are responsible for modulating the entire nitrification process in the estuary. This process is fuelled by the cross feeding among different nitrifiers, which in turn is dictated by nutrient levels especially ammonia. Though nitrification modulates the increasing anthropogenic ammonia concentration the anthropogenic inputs have to be controlled to prevent eutrophication and associated environmental changes.