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.

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

Marine yeast Candida MCCF 101 as feed supplement in aquaculture: nutritional quality, optimization of large scale production and evaluation of its protective effect on Koi carp from Aeromonas infection

Marine yeast have been regarded as safe and showing a beneficial impact on biotechnological process. It provides better nutritional and dietary values indicating their potential application as feed supplements in aquaculture. Brown et al. (1996) evaluated all the marine yeasts characterised with high protein content, carbohydrate, good amino acid composition and high levels of saturated fats. However, there is paucity of information on marine yeasts as feed supplements and no feed formulation has been found either in literature or in market supplemented with them. This statement supported by Zhenming et al. (2006) reported still a lack of feed composed of single cell protein (SCP) from marine yeasts with high content of protein and other nutrients. Recent research has shown that marine yeasts also have highly potential uses in food, feed, medical and biofuel industries as well as marine biotechnology (Chi et al., 2009; 2010). Sajeevan et al. (2006; 2009a) and Sarlin and Philip (2011) demonstrates that the marine yeasts Candida sake served as a high quality, inexpensive nutrient source and it had proven immunostimulatory properties for cultured shrimps. This strain has been made part of the culture collection of National Centre for Aquatic Animal Health, Cochin University of Science and Technology as Candida MCCF 101. Over the years marine yeasts have been gaining increased attention in animal feed industry due to their nutritional value and immune boosting property.Therefore, the present study was undertaken, and focused on the nutritional quality, optimization of large scale production and evaluation of its protective effect on Koi carp from Aeromonas infection