Bivarite burr distributions

The present work is organized into six chapters. Bivariate extension of Burr system is the subject matter of Chapter II. The author proposes to introduce a general structure for the family in two dimensions and present some properties of such a system. Also in Chapter II some new distributions, which are bivariate extension of univariate distributions in Burr (1942) is presented.. In Chapter III, concentrates on characterization problems of different forms of bivariate Burr system. A detailed study of the distributional properties of each member of the Burr system has not been undertaken in literature. With this aim in mind in Chapter IV is discussed with two forms of bivariate Burr III distribution. In Chapter V the author Considers the type XII, type II and type IX distributions. Present work concludes with Chapter VI by pointing out the multivariate extension for Burr system. Also in this chapter the concept of multivariate reversed hazard rates as scalar and vector quantity is introduced.

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

High-momentum proton removal from 16 O and the (e,e'p) cross section

The cross section for the removal of high-momentum protons from 16O is calculated for high missing energies. The admixture of high-momentum nucleons in the 16O ground state is obtained by calculating the single-hole spectral function directly in the finite nucleus with the inclusion of short-range and tensor correlations induced by a realistic meson-exchange interaction. The presence of high-momentum nucleons in the transition to final states in 15N at 60¿100 MeV missing energy is converted to the coincidence cross section for the (e,e¿p) reaction by including the coupling to the electromagnetic probe and the final state interactions of the outgoing proton in the same way as in the standard analysis of the experimental data. Detectable cross sections for the removal of a single proton at these high missing energies are obtained which are considerably larger at higher missing momentum than the corresponding cross sections for the p-wave quasihole transitions. Cross sections for these quasihole transitions are compared with the most recent experimental data available.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

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

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

Bivariate distributions with weighted marginals and reliablity modelling

In this paper, a family of bivariate distributions whose marginals are weighted distributions in the original variables is studied. The relationship between the failure rates of the derived and original models are obtained. These relationships are used to provide some characterizations of specific bivariate models

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Many-body theory of laser-induced ultrafast demagnetization and angular momentum transfer in ferromagnetic transition metals

An electronic theory is developed, which describes the ultrafast demagnetization in itinerant ferromagnets following the absorption of a femtosecond laser pulse. The present work intends to elucidate the microscopic physics of this ultrafast phenomenon by identifying its fundamental mechanisms. In particular, it aims to reveal the nature of the involved spin excitations and angular-momentum transfer between spin and lattice, which are still subjects of intensive debate. In the first preliminary part of the thesis the initial stage of the laser-induced demagnetization process is considered. In this stage the electronic system is highly excited by spin-conserving elementary excitations involved in the laser-pulse absorption, while the spin or magnon degrees of freedom remain very weakly excited. The role of electron-hole excitations on the stability of the magnetic order of one- and two-dimensional 3d transition metals (TMs) is investigated by using ab initio density-functional theory. The results show that the local magnetic moments are remarkably stable even at very high levels of local energy density and, therefore, indicate that these moments preserve their identity throughout the entire demagnetization process. In the second main part of the thesis a many-body theory is proposed, which takes into account these local magnetic moments and the local character of the involved spin excitations such as spin fluctuations from the very beginning. In this approach the relevant valence 3d and 4p electrons are described in terms of a multiband model Hamiltonian which includes Coulomb interactions, interatomic hybridizations, spin-orbit interactions, as well as the coupling to the time-dependent laser field on the same footing. An exact numerical time evolution is performed for small ferromagnetic TM clusters. The dynamical simulations show that after ultra-short laser pulse absorption the magnetization of these clusters decreases on a time scale of hundred femtoseconds. In particular, the results reproduce the experimentally observed laser-induced demagnetization in ferromagnets and demonstrate that this effect can be explained in terms of the following purely electronic non-adiabatic mechanism: First, on a time scale of 10–100 fs after laser excitation the spin-orbit coupling yields local angular-momentum transfer between the spins and the electron orbits, while subsequently the orbital angular momentum is very rapidly quenched in the lattice on the time scale of one femtosecond due to interatomic electron hoppings. In combination, these two processes result in a demagnetization within hundred or a few hundred femtoseconds after laser-pulse absorption.

Der Momentum-Effekt und Momentum-Handelsstrategien

Diese Arbeit weist Momentum-Renditen für europäische Aktien im Zeitraum von 1991 bis 2010 nach, die – je nach Top/Flop-Prozentsatz – vor Kosten zwischen 6 und 19% p.a. liegen. Gleichzeitig liegen mit hohen Standardabweichungen, negativen Schiefe-Werten und hohen Drawdowns drei wesentliche Risikofaktoren vor. Für die Kernuntersuchungen des Top/Flop-Wertes von 5% treten die höchsten Momentum-Renditen von mehr als 10% p.a. für Ranking-Perioden von 80 bis 100 und Holding-Perioden von 60 bis 90 Handelstagen auf. Grundsätzlich sind die extremsten Aktien der Ranking-Periode entscheidend für die Ausprägung des Momentum-Effekts. Gleichzeitig steigen mit zunehmender Eingrenzung des Top/Flop-Wertes die Risiken, was eine Erklärung hoher Momentum-Renditen aus Sicht der Risikoaversions-Theorie nahelegt. Auch die Berücksichtigung zusätzlicher Filterbedingungen (Gleitende Durchschnitte, Handelsvolumen, Low Volatility) ermöglicht leicht höhere Momentum-Renditen bei entsprechend höheren Risiken. Zwischen dem Momentum-Effekt und dem Auftreten von Kurslücken besteht dagegen kein klarer Zusammenhang. Für die praktische Anwendung sind Momentum-Strategien mit dynamischer Positionsverwaltung während der Haltedauer interessant. Untersucht wurden Strategien anhand der eigens programmierten Simulationsverfahren Stopout und Castout sowie eines kombinierten Verfahrens. Im Ergebnis sind – je nach Präferenz des Investors – das Castout- und das kombinierte Verfahren optimal. Für das Rebalancing der Portfolios empfiehlt es sich, zu den entsprechenden Terminen jeweils nur die Short-Seite auf den Startwert zurückzusetzen. Weiterhin zeigen die Untersuchungen, dass deutliche Long-Übergewichtungen bei Momentum-Strategien grundsätzlich von Vorteil sind. Potenzielle Verbesserungen der Ergebnisse können durch weitere Stopp-Abstände, eine Verringerung des Top/Flop-Wertes oder eine längere Ranking-Periode erzielt werden. Weiterhin sind für die Praxis Long-only-Strategien auf Basis von Doppelranking-Verfahren attraktiv, bei denen das Zweitranking nach Standardabweichung oder Rendite/Standardabweichungs-Ratio erfolgt.

Distributions on the simplex

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties