Bayesian Inference in Exponential and Pareto populations in the presence of Outliers

This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.

Parameter identification of a copper-zeolite SCR catalyst model using reactor data

The selective catalytic reduction system is a well established technology for NOx emissions control in diesel engines. A one dimensional, single channel selective catalytic reduction (SCR) model was previously developed using Oak Ridge National Laboratory (ORNL) generated reactor data for an iron-zeolite catalyst system. Calibration of this model to fit the experimental reactor data collected at ORNL for a copper-zeolite SCR catalyst is presented. Initially a test protocol was developed in order to investigate the different phenomena responsible for the SCR system response. A SCR model with two distinct types of storage sites was used. The calibration process was started with storage capacity calculations for the catalyst sample. Then the chemical kinetics occurring at each segment of the protocol was investigated. The reactions included in this model were adsorption, desorption, standard SCR, fast SCR, slow SCR, NH3 Oxidation, NO oxidation and N2O formation. The reaction rates were identified for each temperature using a time domain optimization approach. Assuming an Arrhenius form of the reaction rates, activation energies and pre-exponential parameters were fit to the reaction rates. The results indicate that the Arrhenius form is appropriate and the reaction scheme used allows the model to fit to the experimental data and also for use in real world engine studies.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Stochastic exponential stability of singular linear systems with Markov jump parameters

This paper deals with exponential stability of discrete-time singular systems with Markov jump parameters. We propose a set of coupled generalized Lyapunov equations (CGLE) that provides sufficient conditions to check this property for this class of systems. A method for solving the obtained CGLE is also presented, based on iterations of standard singular Lyapunov equations. We present also a numerical example to illustrate the effectiveness of the approach we are proposing.

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Kinetic parameters associated with self-heating of New Zealand coals under adiabatic conditions

Adiabatic self-heating tests were carried out on five New Zealand coal samples ranging in rank from lignite to high-volatile bituminous. Kinetic parameters of oxidation were obtained front the self-heating curves assuming Arrhenius behaviour. The activation energy E (kJ mol(-1)) and the pre-exponential factor A (s(-1)) were determined in the temperature range of 70-140 degreesC. The activation energy exhibited a definite rank relationship with a minimum E of 55 kJ mol(-1) occurring at a Suggate rank of similar to6.2 corresponding to subbituminous C. Either side of this rank there was a noticeable increase in the activation energy indicating lower reactivity of the coal. A similar rank trend was also observed in the R-70 self-heating rate index values that were taken from the initial portion of the self-heating curve front 40 to 70 degreesC. From these results it is clear that the adiabatic method is capable of providing reliable kinetic parameters of coal oxidation.

Double-Exponential Model of a Photovoltaic Cell with Temperature Dependence

The purpose of the research is the creation of mathematical models in MATLAB based on the double exponential model of the photovoltaic cell. The developed model allows for different physical and environmental parameters. An equivalent circuit of the model includes a photocurrent source, two diodes, and a series and parallel resistance. The paper presents the simulation results for each parameter. The simulation data are displayed graphically and numerical results are saved in a file.

Characteristics of pyridine adsorption on Au(111) and Au(210) by EIS parameters fitting procedure

Some aspects of the application of electrochemical impedance spectroscopy to studies of solid electrode / solution interface, in the absence of faradaic processes, are analysed. In order to perform this analysis, gold electrodes with (111) and (210) crystallographic orientations in an aqueous solution containing 10 mmol dm-3 KF, as supporting electrolyte, and a pyridine concentration varying from 0.01 to 4.6 mmol dm-3, were used. The experimental data was analysed by using EQUIVCRT software, which utilises non-linear least squares routines, attributing to the solid electrode / solution interface behaviour described by an equivalent circuit with a resistance in series with a constant phase element. The results of this fitting procedure were analysed by the dependence on the electrode potential on two parameters: the pre-exponential factor, Y0, and the exponent n f, related with the phase angle shift. By this analysis it was possible to observe that the pyridine adsorption is strongly affected by the crystallographic orientation of the electrode surface and that the extent of deviation from ideal capacitive behaviour is mainly of interfacial origin.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Kinetic parameters for thermal decomposition of supramolecular polymers derived from flunixin-meglumine adducts

Meglumine, (2R,3R,4R,5S)-6-methylaminohexane-1,2,3,4,5-pentol, is a carbohydrate derived from sorbitol in which the hydroxyl group in position one is replaced by a methylamine group. It forms binary adducts with substances having carboxyl groups, which have in common the presence of hydrogen bonding as the main force in the stabilization of these species. During melting, adducts of meglumine with flunixin (2-[[2-methyl-3-(trifluoromethyl)phenyl]amino]pyridine-3-carboxylic acid) polymerize or self-assemble in amorphous supramolecular structures with molecular weights around 2.0 x 10(5) kDa. DSC curves, in a first heating, show isomorphic transitions where the last one at 137 A degrees C for the flunixin-meglumine adduct originated the supramolecular amorphous polymers with glass transition around 49.5 A degrees C. The kinetic parameters for the thermal decomposition step of the polymers were determined by the Capela-Ribeiro non-linear isoconversional method. From data for the TG curves in nitrogen atmosphere and heating rates of 5, 10, 15, and 20 A degrees C min(-1), the E (alpha) and B (alpha) terms could be determined and, consequently, the pre-exponential factor, A(alpha), as well as the kinetic model, g(alpha).

Kinetic parameters for thermal decomposition of microcrystalline, vegetal, and bacterial cellulose

Cellulose can be obtained from innumerable sources such as cotton, trees, sugar cane bagasse, wood, bacteria, and others. The bacterial cellulose (BC) produced by the Gram-negative acetic-acid bacterium Acetobacter xylinum has several unique properties. This BC is produced as highly hydrated membranes free of lignin and hemicelluloses and has a higher molecular weight and higher crystallinity. Here, the thermal behavior of BC, was compared with those of microcrystalline (MMC) and vegetal cellulose (VC). The kinetic parameters for the thermal decomposition step of the celluloses were determined by the Capela-Ribeiro non-linear isoconversional method. From data for the TG curves in nitrogen atmosphere and at heating rates of 5, 10, and 20 A degrees C/min, the E(alpha) and B(alpha) terms could be determined and consequently the pre-exponential factor A(alpha) as well as the kinetic model g(alpha). The pyrolysis of celluloses followed kinetic model g(alpha) = [-ln(1 - alpha)](1.63) on average, characteristic for Avrami-Erofeev with only small differences in activation energy. The fractional value of n may be related to diffusion-controlled growth, or may arise from the distributions of sizes or shapes of the reactant particles.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.