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.

Poverty, Inequality and Natural Resources Degradation

The present study is an attempt to understand the link between natural resource degradation and poverty among people dependent on these resources. This is done by examining the impact of depletion of marine resources on the livelihood and socio-economic condition of the small-scale marine fishery community in South Kerala. In Kerala, nearly ten lakh fisherfolk depend on the marine fishery resources for their livelihood. The overall level of education of the small-scale fishing community is lower than that of the State’s rural population. Almost all the households surveyed, is one way or other, depend on fishery resources for livelihood. Low levels percapita income and high levels of inequality imply the existence of a large proportion of poor people in the community who are vulnerable to external shocks. The study reveals that poverty was comparatively higher among households with no fishing assets, with only one earner, with more than two children, and depending entirely on pensions/remittances. The study has not provided any evidence to show that poverty in the community is the result of depletion of marine resources.

A Bivariate Pareto Distribution with Freund’s Dependence Structure

Department of Statistics, Cochin University of Science and Technology

Income modeling using Quantile Functions

Department of Statistics, Cochin University of Science and Technology

Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

“Rights of Women against Domestic Violence - The Law and Emerging Challenges”

Domestic violence is a gender based violation of human rights having multi- dimensional repercussions in the well- being of individuals in family and society. The Indian legislation to protect the women from domestic violence is significant in providing a mechanism for enforcing positive civil rights of protection and injunction orders to the victims of domestic violence along with the existing remedies of criminal sanctions. However the Act was brought in the backdrop of an established tradition of cohesive and stable family setting. This, in turn, results in the emergence of new issues and challenges which necessitates deeper understandings of indigenous sociocultural institutions in India i.e., marriage and family. This study is an attempt to analyse the Indian law on domestic violence and to assess whether the law addresses and answers the problems of domestic violence effectively in the culture specific setting of India

Gender Bias and Caste Exclusion in Engineering Admission: Inferences from the Engineering Entrance Examination in Kerala

The major problem of the engineering entrance examination is the exclusion of certain sections of the society in social, economic, regional and gender dimensions. This has seldom been taken for analysis towards policy correction. To lessen this problem a minor policy shift was prepared in the year 2011 with a 50–50 proportion in academic marks and entrance marks. The impact of this change is yet to be scrutinized. The data for the study is obtained from the Nodal Centre of Kerala functioning at Cochin University of Science and Technology under the National Technical Manpower Information System and also estimated from the Centralized Allotment Process. The article focuses on two aspects of exclusion based on engineering entrance examination; gender centred as well as caste-linked. Rank order spectral density and Lorenz ratio are used to cognize the exclusion and inequality in community and gender levels in various performance scales. The article unfolds the fact that social status in society coupled with economic affordability to quality education seems to have significant influence in the performance of students in the Kerala engineering entrance examinations. But it also shows that there is wide gender disparity with respect to performance in the high ranking levels irrespective of social groups