Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Optimized allocation of sectionalizing switches and control and protection devices for reliability indices improvement in distribution systems

Reliability of power supply is related, among other factors, to the control and protection devices allocation in feeders of distribution systems. In this way, optimized allocation of sectionalizing switches and protection devices in strategic points of distribution circuits, improves the quality of power supply and the system reliability indices. In this work, it is presented a mixed integer non-linear programming (MINLP) model, with real and binary variables, for the sectionalizing switches and protection devices allocation problem, in strategic sectors, aimed at improving reliability indices, increasing the utilities billing and fulfilling exigencies of regulatory agencies for the power supply. Optimized allocation of protection devices and switches for restoration, allows that those faulted sectors of the system can be isolated and repaired, re-managing loads of the analyzed feeder into the set of neighbor feeders. Proposed solution technique is a Genetic Algorithm (GA) developed exploiting the physical characteristics of the problem. Results obtained through simulations for a real-life circuit, are presented. © 2004 IEEE.

Chronological Monte Carlo-based assessment of distribution system reliability

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties, and in some cases rewards, which introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the Maximum Continuous Interruption Duration per customer (MCID). This paper describes a chronological Monte Carlo simulation approach to evaluate probability distributions of reliability indices, including the MCID, and the corresponding penalties. In order to get the desired efficiency, modern computational techniques are used for modeling (UML -Unified Modeling Language) as well as for programming (Object- Oriented Programming). Case studies on a simple distribution network and on real Brazilian distribution systems are presented and discussed. © Copyright KTH 2006.

Reliability of timber bridges using nailed plywood box beams

The Nailed Box Beam structural efficiency is directly dependent of the flange-web joint behavior, which determines the partial composition of the section, as the displacement between elements reduces the effective rigidity of the section and changes the stress distribution and the total displacement of the section. This work discusses the use of Nailed Plywood Box Beams in small span timber bridges, focusing on the reliability of the beam element. It is presented the results of tests carried out in 21 full scale Nailed Plywood Box Beams. The analysis of maximum load tests results shows that it presents a normal distribution, permitting the characteristic values calculation as the normal distribution theory specifies. The reliability of those elements was analyzed focusing on a timber bridge design, to estimate the failure probability in function of the load level.

Network reconfiguration of distribution systems using metaheuristics and reliability measures

In an evermore competitive environment, power distribution companies need to continuously monitor and improve the reliability indices of their systems. The network reconfiguration (NR) of a distribution system is a technique that well adapts to this new deregulated environment for it allows improvement of system reliability indices without the onus involved in procuring new equipment. This paper presents a reliability-based NR methodology that uses metaheuristic techniques to search for the optimal network configuration. Three metaheuristics, i.e. Tabu Search, Evolution Strategy, and Differential Evolution, are tested using a Brazilian distribution network and the results are discussed. © 2009 IEEE.

Improving the grid operation and reliability cost of distribution systems with dispersed generation

In this work, a mathematical model to analyze the impact of the installation and operation of dispersed generation units in power distribution systems is proposed. The main focus is to determine the trade-off between the reliability and operational costs of distribution networks when the operation of isolated areas is allowed. In order to increase the system operator revenue, an optimal power flow makes use of the different energy prices offered by the dispersed generation connected to the grid. Simultaneously, the type and location of the protective devices initially installed on the protection system are reconfigured in order to minimize the interruption and expenditure of adjusting the protection system to conditions imposed by the operation of dispersed units. The interruption cost regards the unsupplied energy to customers in secure systems but affected by the normal tripping of protective devices. Therefore, the tripping of fuses, reclosers, and overcurrent relays aims to protect the system against both temporary and permanent fault types. Additionally, in order to reduce the average duration of the system interruption experienced by customers, the isolated operation of dispersed generation is allowed by installing directional overcurrent relays with synchronized reclose capabilities. A 135-bus real distribution system is used in order to show the advantages of using the mathematical model proposed. © 1969-2012 IEEE.

Análise Bayesiana para a distribuição Exponencial-Logarítmica

Pós-graduação em Matematica Aplicada e Computacional - FCT

Análise clássica e bayesiana do modelo Weibull modificado generalizado

Pós-graduação em Matematica Aplicada e Computacional - FCT

The employment situation in Latin America and the Caribbean: Labour productivity and distribution issues

Although the economies of Latin America and the Caribbean grew more slowly in 2011 than in 2010, there were some improvements on the employment front. Workers benefited from the region’s satisfactory economic performance in an increasingly complex international setting. The unemployment rate fell from 7.3% in 2010 to 6.7% in 2011 thanks to a halfpercentage- point gain in the urban employment rate. Both rates are at levels that have not been seen for a long time. The proportion of formal jobs with social benefits rose as well, and underemployment declined. The average wage and the minimum wage both increased in real terms, albeit only moderately. Economic performance and the employment situation varied widely among the subregions. The unemployment rate dropped by 0.6 percentage points in South America but 0.4 percentage points in the countries of the northern part of Latin America. In the countries of the Caribbean, the employment rate was up by 0.2 percentage points. The data show that substantial labour market gaps and serious labour-market insertion issues remain. This is especially the case for women and young people, for whom unemployment rates and other labour indicators are still unfavourable. The second part of this report looks at whether the fruits of economic growth and rising productivity have been distributed equitably between workers and companies. Between 2002 and 2008 (the most recent expansionary economic cycle), wages as a percentage of GDP fell in 13 of the 21 countries of the region for which data are available and rose in just 8. This points to redistribution that is unfavourable to workers, which is worrying in a region which already has the most unequal distribution of income in the world. Underlying this trend is the fact that, worldwide, wages have grown less than productivity. Beyond the ethical dimension of this issue, it jeopardizes the social and economic sustainability of growth. For example, one of the root causes of the recent financial crisis was that households in the United States responded to declining wage income by borrowing more to pay for consumption and housing. This turned out to be unsustainable in the long run. Over time, it undermines the labour market’s contribution to the efficient allocation of resources and its distributive function, too, with negative consequences for democratic governance. Among the triggers of this distributive worsening most often cited in the global debate are market deregulation and its impact on financial globalization, technological change that favours capital over labour, and the weakening of labour institutions. What is needed here is a public policy effort to help keep wage increases from lagging behind increases in productivity. Some countries of the region, especially in South America, saw promising developments during the second half of the 2000s in the form of a positive trend reversal in wages as a percentage of GDP. One example is Brazil, where a minimum wage policy tailored to the dynamics of the domestic market is considered to be one of the factors behind an upturn in the wage share of GDP. The region needs to grow more and better. Productivity must grow at a steady pace, to serve as the basis for sustained improvements in the well-being of the populace and to narrow the gap between the economies of Latin America and the Caribbean and the more advanced economies. And inequality must be decreased; this could be achieved by closing the productivity gap between upgraded companies and the many firms whose productivity is low. As set out in this report, the region made some progress between 2002 and 2010, with labour productivity rising at the rate of 1.5% a year. But this progress falls short of that seen in other regions such as Sub-Saharan Africa (2.1%) and, above all, East Asia (8.3%, not counting Japan and the Republic of Korea). Moreover, in many of the countries of the region these gains have not been distributed equitably. Therein lies a dual challenge that must be addressed: continue to increase productivity while enhancing the mechanisms for distributing gains in a way that will encourage investment and boost worker and household income. The Economic Commission for Latin America and the Caribbean (ECLAC) and the International Labour Organization (ILO) estimate that the pace of economic growth in the region will be slightly slower in 2012 than in 2011, in a global economic scenario marked by the cooling of several of the main economic engines and a high degree of uncertainty concerning, above all, prospects for the euro zone. The region is expected to continue to hold up well to this worsening scenario, thanks to policies that leveraged more favourable conditions in the past. This will be felt in the labour markets, as well, so expectations are that unemployment will edge down by as much as two tenths of a decimal point.

Influence of abutment-to-fixture design on reliability and failure mode of all-ceramic crown systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A aplicação da distribuição exponencial geométrica estendida para modelagem de dados pluviométricos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Benthic foraminiferal distribution on the southeastern Brazilian shelf and upper slope

Foraminiferal data were obtained from 66 samples of box cores on the southeastern Brazilian upper margin (between 23.8A degrees-25.9A degrees S and 42.8A degrees-46.13A degrees W) to evaluate the benthic foraminiferal fauna distribution and its relation to some selected abiotic parameters. We focused on areas with different primary production regimes on the southern Brazilian margin, which is generally considered as an oligotrophic region. The total density (D), richness (R), mean diversity (H) over bar`, average living depth (ALD(X) ) and percentages of specimens of different microhabitats (epifauna, shallow infauna, intermediate infauna and deep infauna) were analyzed. The dominant species identified were Uvigerina spp., Globocassidulina subglobosa, Bulimina marginata, Adercotryma wrighti, Islandiella norcrossi, Rhizammina spp. and Brizalina sp.. We also established a set of mathematical functions for analyzing the vertical foraminiferal distribution patterns, providing a quantitative tool that allows correlating the microfaunal density distributions with abiotic factors. In general, the cores that fit with pure exponential decaying functions were related to the oligotrophic conditions prevalent on the Brazilian margin and to the flow of the Brazilian Current (BC). Different foraminiferal responses were identified in cores located in higher productivity zones, such as the northern and the southern region of the study area, where high percentages of infauna were encountered in these cores, and the functions used to fit these profiles differ appreciably from a pure exponential function, as a response of the significant living fauna in deeper layers of the sediment. One of the main factors supporting the different foraminiferal assemblage responses may be related to the differences in primary productivity of the water column and, consequently, in the estimated carbon flux to the sea floor. Nevertheless, also bottom water velocities, substrate type and water depth need to be considered.

The McDonald inverted beta distribution

We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.