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.

An analogue of the logistic map in two dimensions

This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

A Comparative Study Of The Organisation And Management Of Notihed Markets In Bangladesh With The Organisation And Management Of Regulated Markets In West Bengal India

For improving agricultural marketing, which has been discussed in the previous chapter, the Government has intervened in different ways. The direct regulatory role through the regulation of markets and market practices is one of the ways in which governmental intervention can improve agricultural marketing. This study is an enquiry of the direct regulatory role of the government through regulation of markets and market practices. By restructuring the operational methods and redesigning the existing physical markets, this system gives direct benefit to the cultivating class and protects them from the market manipulations of organised and powerful private traders. If traders do not continue their trade for the time being they will not be affected financially, because they are resourceful or financially solvent. On the other hand, Cultivators must sell their produce immediately after harvesting for the lack of additional facilities or to satisfy other needs for which finance is required. Another important reason is that Cultivators/farmers are not organised and because of lack of their organisation, they sell their produces individually. In this situation, a farmer is helpless when astute traders indulge in manipulations at the time of purchase of the produces. So it is the government's obligation to protect the interest of the farmers. Protection of the farmer/cultivator is necessary not only from the point of social justice but also from that of economic growth. If the farmers are assured of a remunerative or incentive price for their produce, they will get the inspiration to produce more and through more production, economy will be developed and the nation as a whole will be benefitted. This study will examine the management system of the markets through the direct regulatory role played by the governments to control markets and market practices in West Bengal and Bangladesh.