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.

Evidence for polaron conduction in nanostructured manganese ferrite

Nanoparticles of manganese ferrite were prepared by the chemical co-precipitation technique. The dielectric parameters, namely, real and imaginary dielectric permittivity (ε and ε ), ac conductivity (σac) and dielectric loss tangent (tan δ), were measured in the frequency range of 100 kHz–8MHz at different temperatures. The variations of dielectric dispersion (ε ) and dielectric absorption (ε ) with frequency and temperature were also investigated. The variation of dielectric permittivity with frequency and temperature followed the Maxwell–Wagner model based on interfacial polarization in consonance with Koops phenomenological theory. The dielectric loss tangent and hence ε exhibited a relaxation at certain frequencies and at relatively higher temperatures. The dispersion of dielectric permittivity and broadening of the dielectric absorption suggest the possibility of a distribution of relaxation time and the existence of multiple equilibrium states in manganese ferrite. The activation energy estimated from the dielectric relaxation is found to be high and is characteristic of polaron conduction in the nanosized manganese ferrite. The ac conductivity followed a power law dependence σac = Bωn typical of charge transport assisted by a hopping or tunnelling process. The observed minimum in the temperature dependence of the frequency exponent n strongly suggests that tunnelling of the large polarons is the dominant transport process

Mechanism of ac conduction in nanostructured manganese zinc mixed ferrites

Mn1−xZnxFe2O4 nanoparticles (x = 0 to 1) were synthesized by the wet chemical co-precipitation technique. X-ray diffraction and transmission electron microscopy and high resolution transmission electron microscopy were effectively utilized to investigate the different structural parameters. The ac conductivity of nanosized Mn1−xZnxFe2O4 were investigated as a function of frequency, temperature and composition. The frequency dependence of ac conductivity is analysed by the power law σ(ω)ac = Bωn which is typical for charge transport by hopping or tunnelling processes. The temperature dependence of frequency exponent n was investigated to understand the conduction mechanism in different compositions. The conduction mechanisms are mainly based on polaron hopping conduction

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

Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables