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.

Spatial and temporal characteristics of rain intensity in the peninsular Malaysia using TRMM rain rate

The present study is focused on the intensity distribution of rainfall in different classes and their contribution to the total seasonal rainfall. In addition, we studied the spatial and diurnal variation of the rainfall in the study areas. For the present study, we retrieved data from TRMM (Tropical Rain Measuring Mission) rain rate available in every 3 h temporal and 25 km spatial resolutions. Moreover, station rainfall data is used to validate the TRMM rain rate and found significant correlation between them (linear correlation coefficients are 0.96, 0.85, 0.75 and 0.63 for the stations Kota Bharu, Senai, Cameron highlands and KLIA, respectively). We selected four areas in the Peninsular Malaysia and they are south coastal, east coastal, west coastal and highland regions. Diurnal variation of frequency of rain occurrence is different for different locations. We noticed bimodal variation in the coastal areas in most of the seasons and unimodal variation in the highland/inland area. During the southwest monsoon period in the west coastal stations, there is no distinct diurnal variation. The distribution of different intensity classes during different seasons are explained in detail in the results