Analysis of the distribution of the number of bidders in construction contract auctions

The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark-up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent 30 years, little progress has been made, due principally to the absence of new ideas and perspectives. The debate is resumed by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to ensure universality, a novel approach is developed and tested by using a unique set of 12 construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study.

Thermodynamic and statistical analysis of soybean oil extraction process using renewable solvent

The main goal of this work was to evaluate thermodynamic parameters of the soybean oil extraction process using ethanol as solvent. The experimental treatments were as follows: aqueous solvents with water contents varying from 0 to 13% (mass basis) and extraction temperature varying from 50 to 100 degrees C. The distribution coefficients of oil at equilibrium have been used to calculate enthalpy, entropy and free energy changes. The results indicate that oil extraction process with ethanol is feasible and spontaneous, mainly under higher temperature. Also, the influence of water level in the solvent and temperature were analysed using the response surface methodology (RSM). It can be noted that the extraction yield was highly affected by both independent variables. A joint analysis of thermodynamic and RSM indicates the optimal level of solvent hydration and temperature to perform the extraction process.

On the mass distribution of neutron stars

The distribution of masses for neutron stars is analysed using the Bayesian statistical inference, evaluating the likelihood of the proposed Gaussian peaks by using 54 measured points obtained in a variety of systems. The results strongly suggest the existence of a bimodal distribution of the masses, with the first peak around 1.37 M(circle dot) and a much wider second peak at 1.73 M(circle dot). The results support earlier views related to the different evolutionary histories of the members for the first two peaks, which produces a natural separation (even if no attempt to `label` the systems has been made here). They also accommodate the recent findings of similar to M(circle dot) masses quite naturally. Finally, we explore the existence of a subgroup around 1.25 M(circle dot), finding weak, if any, evidence for it. This recently claimed low-mass subgroup, possibly related to the O-Mg-Ne core collapse events, has a monotonically decreasing likelihood and does not stand out clearly from the rest of the sample.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Epsilon Birnbaum-Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum-Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427-443, 2005). The extension allows generating Birnbaun-Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88-95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 Elsevier B.V. All rights reserved.

An extension of the generalized Birnbaum-Saunders distribution

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Diaz-Garcia, J.A., Leiva-Sanchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered. (C) 2008 Elsevier B.V. All rights reserved.

An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Heuristic optimization of the p-median problem and population re-distribution

This thesis contributes to the heuristic optimization of the p-median problem and Swedish population redistribution.   The p-median model is the most representative model in the location analysis. When facilities are located to a population geographically distributed in Q demand points, the p-median model systematically considers all the demand points such that each demand point will have an effect on the decision of the location. However, a series of questions arise. How do we measure the distances? Does the number of facilities to be located have a strong impact on the result? What scale of the network is suitable? How good is our solution? We have scrutinized a lot of issues like those. The reason why we are interested in those questions is that there are a lot of uncertainties in the solutions. We cannot guarantee our solution is good enough for making decisions. The technique of heuristic optimization is formulated in the thesis.   Swedish population redistribution is examined by a spatio-temporal covariance model. A descriptive analysis is not always enough to describe the moving effects from the neighbouring population. A correlation or a covariance analysis is more explicit to show the tendencies. Similarly, the optimization technique of the parameter estimation is required and is executed in the frame of statistical modeling. 

Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability

A number of recent works have introduced statistical methods for detecting genetic loci that affect phenotypic variability, which we refer to as variability-controlling quantitative trait loci (vQTL). These are genetic variants whose allelic state predicts how much phenotype values will vary about their expected means. Such loci are of great potential interest in both human and non-human genetic studies, one reason being that a detected vQTL could represent a previously undetected interaction with other genes or environmental factors. The simultaneous publication of these new methods in different journals has in many cases precluded opportunity for comparison. We survey some of these methods, the respective trade-offs they imply, and the connections between them. The methods fall into three main groups: classical non-parametric, fully parametric, and semi-parametric two-stage approximations. Choosing between alternatives involves balancing the need for robustness, flexibility, and speed. For each method, we identify important assumptions and limitations, including those of practical importance, such as their scope for including covariates and random effects. We show in simulations that both parametric methods and their semi-parametric approximations can give elevated false positive rates when they ignore mean-variance relationships intrinsic to the data generation process. We conclude that choice of method depends on the trait distribution, the need to include non-genetic covariates, and the population size and structure, coupled with a critical evaluation of how these fit with the assumptions of the statistical model.

Statistical modelling of extreme rainfall in Madeira Island

Extreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.

Soil sampling intensity and spatial distribution pattern of soils attributes and corn yield in no-tillage system

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