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.

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Bidentates versus monodentates in asymmetric hydrogenation catalysis: synergic effects on rate and allosteric effects on enantioselectivity

C-1-Symmetric phosphino/phosphonite ligands are prepared by the reactions of Ph2P(CH2)(2)P(NMe2)(2) with (S)-1,11'-bi-2-naphthol (to give L-A) or (S)-10,10'-bi-9-phenanthrol (to give L-B). Racemic 10,10'-bi-9-phenanthrol is synthesized in three steps from phenanthrene in 44% overall yield. The complexes [PdCl2(L-A,L-B)] (1a,b), [PtCl2(L-A,L-B)] (2a,b), [Rh(cod)(L-A,L-B)]BF4 (3a,b) and [Rh(L-A,L-B)(2)]BF4 (4a,b) are reported and the crystal structure of la has been determined. A P-31 NMR study shows that M, a 1:1 mixture of the monodentates, PMePh2 and methyl monophosphonite L-1a (based on (S)-1,11'-bi-2-naphthol), reacts with 1 equiv of [Rh(cod)(2)]BF4 to give the heteroligand complex [Rh(cod)(PMePh2)(L-1a)]BF4 (5) and homoligand complexes [Rh(cod)(PMePh2)(2)]BF4 (6) and [Rh(cod)(L-1a)(2)]BF4 (7) in the ratio 2:1:1. The same mixture of 5-7 is obtained upon mixing the isolated homoligand complexes 6 and 7 although the equilibrium is only established rapidly in the presence of an excess of PMePh2. The predominant species 5 is a monodentate ligand complex analogue of the chelate 3a. When the mixture of 5-7 is exposed to 5 atm H-2 for 1 h (the conditions used for catalyst preactivation in the asymmetric hydrogenation studies), the products are identified as the solvento species [Rh(PMePh2)(L-1a)(S)(2)]BF4 (5'), [Rh(S)(2)(PMePh2)(2)]BF4 (6') and [Rh(S)(2)(L-1a)(2)]BF4 (7') and are formed in the same 2:1:1 ratio. The reaction of M with 0.5 equiv of [Rh(cod)(2)]BF4 gives exclusively the heteroligand complex cis-[Rh(PMePh2)(2)(L-1a)(2)]BF4 (8), an analogue of 4a. The asymmetric hydrogenation of dehydroamino acid derivatives catalyzed by 3a,b is reported, and the enantioselectivities are compared with those obtained with (a) chelate catalysts derived from analogous diphosphonite ligands L-2a and L-2b, (b) catalysts based on methyl monophosphonites L-1a and L-1b, and (c) catalysts derived from mixture M. For the cinnamate and acrylate substrates studied, the catalysts derived from the phosphino/phosphonite bidentates L-A,L-B generally give superior enantioselectivities to the analogous diphosphonites L-2a and L-2b; these results are rationalized in terms of delta/lambda-chelate conformations and allosteric effects of the substrates. The rate of hydrogenation of acrylate substrate A with heterochelate 3a is significantly faster than with the homochelate analogues [Rh(L-2a)(cod)]BF4 and [Rh(dppe)(cod)]BF4. A synergic effect on the rate is also observed with the monodentate analogues: the rate of hydrogenation with the mixture containing predominantly heteroligand complex 5 is faster than with the monophosphine complex 6 or monophosphonite complex 7. Thus the hydrogenation catalysis carried out with M and [Rh(cod)(2)]BF4 is controlled by the dominant and most efficient heteroligand complex 5. In this study, the heterodiphos chelate 3a is shown to be more efficient and gives the opposite sense of optical induction t the heteromonophos analogue

Insights into redox cycling of sulfur and iron in peatlands using high-resolution diffusive equilibrium thin film (DET) gel probe sampling

High spatial resolution vertical profiles of pore-water chemistry have been obtained for a peatland using diffusive equilibrium in thin films (DET) gel probes. Comparison of DET pore-water data with more traditional depth-specific sampling shows good agreement and the DET profiling method is less invasive and less likely to induce mixing of pore-waters. Chloride mass balances as water tables fell in the early summer indicate that evaporative concentration dominates and there is negligible lateral flow in the peat. Lack of lateral flow allows element budgets for the same site at different times to be compared. The high spatial resolution of sampling also enables gradients to be observed that permit calculations of vertical fluxes. Sulfate concentrations fall at two sites with net rates of 1.5 and 5.0nmol cm− 3 day− 1, likely due to a dominance of bacterial sulfate reduction, while a third site showed a net gain in sulfate due to oxidation of sulfur over the study period at an average rate of 3.4nmol cm− 3 day− 1. Behaviour of iron is closely coupled to that of sulfur; there is net removal of iron at the two sites where sulfate reduction dominates and addition of iron where oxidation dominates. The profiles demonstrate that, in addition to strong vertical redox related chemical changes, there is significant spatial heterogeneity. Whilst overall there is evidence for net reduction of sulfate within the peatland pore-waters, this can be reversed, at least temporarily, during periods of drought when sulfide oxidation with resulting acid production predominates.

Spin equilibrium and outflows in young stellar objects

We present N-body simulations of accretion discs about young stellar objects (YSOs). The simulation includes the presence of a magnetic loop structure on the central star which interacts with the particles by means of a magnetic drag force. We find that an equilibrium spin rate is achieved when the corotation radius coincides with the edge of the loop. This spin rate is consistent with observed values for TTauri stars, being an order of magnitude less than the breakup value. The material ejected from the system by the rotating loop has properties consistent with the observed molecular outflows, given the presence of a suitable containing cavity.

Changes of the equilibrium line altitude since the Little Ice Age in the Nepalese Himalayas

Changes of the equilibrium-line altitude (ELA) since the end of the Little Ice Age (LIA) in eastern Nepal have been studied using glacier inventory data. The toe-to-headwall altitude ratios (THARs) for individual glaciers were calculated for 1992, and used to estimate the ELA in 1959 and at the end of the LIA. THAR for debris-free glaciers is found to be smaller than for debris-covered glaciers. The ELAs for debris-covered glaciers are higher than those for debris-free glaciers in eastern Nepal. There is considerable variation in the reconstructed change in ELA (ΔELA) between glaciers within specific regions and between regions. This is not related to climate gradients, but results from differences in glacier aspect: southeast- and south-facing glaciers show larger ΔELAs in eastern Nepal than north- or west-facing glaciers. The data suggest that the rate of ELA rise may have accelerated in the last few decades. The limited number of climate records from Nepal, and analyses using a simple ELA–climate model, suggest that the higher rate of the ΔELA between 1959 and 1992 is a result of increased warming that occurred after the 1970s at higher altitudes in Nepal.

Real exchange rate misalignments

This paper characterizes episodes of real appreciations and depreciations for a sample of 85 countries, approximately from 1960 to 1998. First, the equilibrium real exchange rate series are constructed for each country using Goldfajn and Valdes (1999) methodology (cointegration with fundamentals). Then, departures from equilibrium real exchange rate (misalignments) are obtained, and a Markov Switching Model is used to characterize the misalignments series as stochastic autoregressive processes governed by two states representing di¤erent means. Three are the main results we …nd: …rst, no evidence of di¤erent regimes for misalignment is found in some countries, second, some countries present one regime of no misalignment (tranquility) and the other regime with misalignment (crisis), and, third, for those countries with two misalignment regimes, the lower mean misalignment regime (appreciated) have higher persistence that the higher mean one (depreciated).

The political economy of exchange rate in Brazil

This paper reviews part of the political economy literature on exchange rate policy relevant to understanding the political motivations behind the Brazilian exchange rate policy. We shall first examine the distributive role of the exchange rate, and the way it unfolds in terms of the desired political goals. We will follow by analyzing exchange policy as indicative of government effciency prior to elections. Finally, we discuss fiscal policy from the point of view of political economy, in which the exchange rate results from the macroeconomic equilibrium. Over this review, the Brazilian exchange rate policy is discussed in light of the theories presented.

Optimal exchange rate policy, optimal incomplete taxation and business cycles

Implementation and collapse of exchange rate pegging schemes are recur- rent events. A currency crisis (pegging) is usually followed by an economic downturn (boom). This essay explains why a benevolent government should pursue Þscal and monetary policies that lead to those recurrent currency crises and subsequent periods of pegging. It is shown that the optimal policy induces a competitive equilibrium that displays a boom in periods of below average de- valuation and a recession in periods of above average devaluation. A currency crisis (pegging) can be understood as an optimal policy answer to a recession (boom).

The effects of government deficit on equilibrium real exchange rates and stock prices

This paper studies the effect of government deficits on equilibrium real exchange rates and stock prices. The theoretical part modifies a two-country cash-in-advance model like used in Lucas(1982) and Sargent(1987) in order to accommodate an exchange rate market and a government that pursues fiscal and monetary policy targets. The implied result is that unanticipated shocks in government deficits raise expectations of both taxes and inflation and, therefore, are associated with real exchange rate devaluations and lower stock prices. This finding is strongly supported by empirical evidence for a group of 19 countries, representing 76% of world production

Comparing equilibrium real interest rates : different approaches to measure Brazilian rates

Despite the difficulties involved in the precise determination of equilibrium real interest rates, it seems clear that nominal interest rates has been higher in Brazil than in similar emerging economies. This paper aims to shed light on the possible reasons for this feature of the Brazilian economy. We extend Miranda and Muinhos (2003) one-country study to a sample of 20 countries, using many methods to compare measures of the real interest: (i) extracting equilibrium interest rates from IS curves; (ii) extracting steady state interest rates from marginal product of capital; (iii) capturing relevant variables and the fixed effects having real interest rates as dependent variable in a panel for emerging countries; and (iv) extracting inflation expectation from the spread between fixed rate and inflation-indexed treasure notes.

Monetary dynamics in a general equilibrium version of the Baumol-Tobin model

I study the welfare cost of inflation and the effect on prices after a permanent increase in the interest rate. In the steady state, the real money demand is homogeneous of degree one in income and its interest-rate elasticity is approximately equal to −1/2. Consumers are indifferent between an economy with 10% p.a. inflation and one with zero inflation if their income is 1% higher in the first economy. A permanent increase in the interest rate makes the price level to drop initially and inflation to adjust slowly to its steady state level.

Assessing interdependence among countries' fundamentals and its implications for exchange rate misalignment estimates: An empirical exercise based on GVAR

Exchange rates are important macroeconomic prices and changes in these rates a ect economic activity, prices, interest rates, and trade ows. Methodologies have been developed in empirical exchange rate misalignment studies to evaluate whether a real e ective exchange is overvalued or undervalued. There is a vast body of literature on the determinants of long-term real exchange rates and on empirical strategies to implement the equilibrium norms obtained from theoretical models. This study seeks to contribute to this literature by showing that the global vector autoregressions model (GVAR) proposed by Pesaran and co-authors can add relevant information to the literature on measuring exchange rate misalignment. Our empirical exercise suggests that the estimate exchange rate misalignment obtained from GVAR can be quite di erent to that using the traditional cointegrated time series techniques, which treat countries as detached entities. The di erences between the two approaches are more pronounced for small and developing countries. Our results also suggest a strong interdependence among eurozone countries, as expected

Addressing important econometric issues on how to construct theoretical based exchange rate misalignment estimates

Exchange rate misalignment assessment is becoming more relevant in recent period particularly after the nancial crisis of 2008. There are di erent methodologies to address real exchange rate misalignment. The real exchange misalignment is de ned as the di erence between actual real e ective exchange rate and some equilibrium norm. Di erent norms are available in the literature. Our paper aims to contribute to the literature by showing that Behavioral Equilibrium Exchange Rate approach (BEER) adopted by Clark & MacDonald (1999), Ubide et al. (1999), Faruqee (1994), Aguirre & Calderón (2005) and Kubota (2009) among others can be improved in two following manners. The rst one consists of jointly modeling real e ective exchange rate, trade balance and net foreign asset position. The second one has to do with the possibility of explicitly testing over identifying restrictions implied by economic theory and allowing the analyst to show that these restrictions are not falsi ed by the empirical evidence. If the economic based identifying restrictions are not rejected it is also possible to decompose exchange rate misalignment in two pieces, one related to long run fundamentals of exchange rate and the other related to external account imbalances. We also discuss some necessary conditions that should be satis ed for disrcarding trade balance information without compromising exchange rate misalignment assessment. A statistical (but not a theoretical) identifying strategy for calculating exchange rate misalignment is also discussed. We illustrate the advantages of our approach by analyzing the Brazilian case. We show that the traditional approach disregard important information of external accounts equilibrium for this economy.

Regional integration and the issue of choosing an appropriate exchange-rate regime in Latin America

Includes bibliography