A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ���addition���. In particular an associative, binary operator ��� * ��� is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

A generalization of Student���s t-distribution from the viewpoint of special functions

Student���s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

On the Noise Model of Support Vector Machine Regression

Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s $epsilon$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions.

Una aproximaci��n de la variable aleatoria a procesos de toma de decisi��n que implican condiciones de riesgo e incertidumbre

La variable aleatoria es una funci��n matem��tica que permite asignar valores num��ricos a cada uno de los posibles resultados obtenidos en un evento de naturaleza aleatoria. Si el n��mero de estos resultados se puede contar, se tiene un conjunto discreto; por el contrario, cuando el n��mero de resultados es infinito y no se puede contar, se tiene un conjunto continuo. El objetivo de la variable aleatoria es permitir adelantar estudios probabil��sticos y estad��sticos a partir del establecimiento de una asignaci��n num��rica a trav��s de la cual se identifiquen cada uno de los resultados que pueden ser obtenidos en el desarrollo de un evento determinado. El valor esperado y la varianza son los par��metros por medio de los cuales es posible caracterizar el comportamiento de los datos reunidos en el desarrollo de una situaci��n experimental; el valor esperado permite establecer el valor sobre el cual se centra la distribuci��n de la probabilidad, mientras que la varianza proporciona informaci��n acerca de la manera como se distribuyen los datos obtenidos. Adicionalmente, las distribuciones de probabilidad son funciones num��ricas asociadas a la variable aleatoria que describen la asignaci��n de probabilidad para cada uno de los elementos del espacio muestral y se caracterizan por ser un conjunto de par��metros que establecen su comportamiento funcional, es decir, cada uno de los par��metros propios de la distribuci��n suministra informaci��n del experimento aleatorio al que se asocia. El documento se cierra con una aproximaci��n de la variable aleatoria a procesos de toma de decisi��n que implican condiciones de riesgo e incertidumbre.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Conceptual design of wastewater treatment plants using multiple objectives

La implementaci�� de la Directiva Europea 91/271/CEE referent a tractament d'aig��es residuals urbanes va promoure la construcci�� de noves instal��lacions al mateix temps que la introducci�� de noves tecnologies per tractar nutrients en ��rees designades com a sensibles. Tant el disseny d'aquestes noves infraestructures com el redisseny de les ja existents es va portar a terme a partir d'aproximacions basades fonamentalment en objectius econ��mics degut a la necessitat d'acabar les obres en un per��ode de temps relativament curt. Aquests estudis estaven basats en coneixement heur��stic o correlacions num��riques provinents de models determin��stics simplificats. Aix�� doncs, moltes de les estacions depuradores d'aig��es residuals (EDARs) resultants van estar caracteritzades per una manca de robustesa i flexibilitat, poca controlabilitat, amb freq��ents problemes microbiol��gics de separaci�� de s��lids en el decantador secundari, elevats costos d'operaci�� i eliminaci�� parcial de nutrients allunyant-les de l'��ptim de funcionament. Molts d'aquestes problemes van sorgir degut a un disseny inadequat, de manera que la comunitat cient��fica es va adonar de la import��ncia de les etapes inicials de disseny conceptual. Precisament per aquesta ra��, els m��todes tradicionals de disseny han d'evolucionar cap a sistemes d'avaluaci�� mes complexos, que tinguin en compte m��ltiples objectius, assegurant aix�� un millor funcionament de la planta. Tot i la import��ncia del disseny conceptual tenint en compte m��ltiples objectius, encara hi ha un buit important en la literatura cient��fica tractant aquest camp d'investigaci��. L'objectiu que persegueix aquesta tesi ��s el de desenvolupar un m��tode de disseny conceptual d'EDARs considerant m��ltiples objectius, de manera que serveixi d'eina de suport a la presa de decisions al seleccionar la millor alternativa entre diferents opcions de disseny. Aquest treball de recerca contribueix amb un m��tode de disseny modular i evolutiu que combina diferent t��cniques com: el proc��s de decisi�� jer��rquic, an��lisi multicriteri, optimaci�� preliminar multiobjectiu basada en an��lisi de sensibilitat, t��cniques d'extracci�� de coneixement i mineria de dades, an��lisi multivariant i an��lisi d'incertesa a partir de simulacions de Monte Carlo. Aix�� s'ha aconseguit subdividint el m��tode de disseny desenvolupat en aquesta tesis en quatre blocs principals: (1) generaci�� jer��rquica i an��lisi multicriteri d'alternatives, (2) an��lisi de decisions cr��tiques, (3) an��lisi multivariant i (4) an��lisi d'incertesa. El primer dels blocs combina un proc��s de decisi�� jer��rquic amb an��lisi multicriteri. El proc��s de decisi�� jer��rquic subdivideix el disseny conceptual en una s��rie de q��estions mes f��cilment analitzables i avaluables mentre que l'an��lisi multicriteri permet la consideraci�� de diferent objectius al mateix temps. D'aquesta manera es redueix el nombre d'alternatives a avaluar i fa que el futur disseny i operaci�� de la planta estigui influenciat per aspectes ambientals, econ��mics, t��cnics i legals. Finalment aquest bloc inclou una an��lisi de sensibilitat dels pesos que proporciona informaci�� de com varien les diferents alternatives al mateix temps que canvia la import��ncia relativa del objectius de disseny. El segon bloc engloba t��cniques d'an��lisi de sensibilitat, optimitzaci�� preliminar multiobjectiu i extracci�� de coneixement per donar suport al disseny conceptual d'EDAR, seleccionant la millor alternativa un cop s'han identificat decisions cr��tiques. Les decisions cr��tiques s��n aquelles en les que s'ha de seleccionar entre alternatives que compleixen de forma similar els objectius de disseny per�� amb diferents implicacions pel que respecte a la futura estructura i operaci�� de la planta. Aquest tipus d'an��lisi proporciona una visi�� m��s ��mplia de l'espai de disseny i permet identificar direccions desitjables (o indesitjables) cap on el proc��s de disseny pot derivar. El tercer bloc de la tesi proporciona l'an��lisi multivariant de les matrius multicriteri obtingudes durant l'avaluaci�� de les alternatives de disseny. Espec��ficament, les t��cniques utilitzades en aquest treball de recerca engloben: 1) an��lisi de conglomerats, 2) an��lisi de components principals/an��lisi factorial i 3) an��lisi discriminant. Com a resultat ��s possible un millor acc��s a les dades per realitzar la selecci�� de les alternatives, proporcionant m��s informaci�� per a una avaluaci�� mes efectiva, i finalment incrementant el coneixement del proc��s d'avaluaci�� de les alternatives de disseny generades. En el quart i ��ltim bloc desenvolupat en aquesta tesi, les diferents alternatives de disseny s��n avaluades amb incertesa. L'objectiu d'aquest bloc ��s el d'estudiar el canvi en la presa de decisions quan una alternativa ��s avaluada incloent o no incertesa en els par��metres dels models que descriuen el seu comportament. La incertesa en el par��metres del model s'introdueix a partir de funcions de probabilitat. Despr��s es porten a terme simulacions Monte Carlo, on d'aquestes distribucions se n'extrauen n��meros aleatoris que es subsisteixen pels par��metres del model i permeten estudiar com la incertesa es propaga a trav��s del model. Aix�� ��s possible analitzar la variaci�� en l'acompliment global dels objectius de disseny per a cada una de les alternatives, quines s��n les contribucions en aquesta variaci�� que hi tenen els aspectes ambientals, legals, econ��mics i t��cnics, i finalment el canvi en la selecci�� d'alternatives quan hi ha una variaci�� de la import��ncia relativa dels objectius de disseny. En comparaci�� amb les aproximacions tradicionals de disseny, el m��tode desenvolupat en aquesta tesi adre��a problemes de disseny/redisseny tenint en compte m��ltiples objectius i m��ltiples criteris. Al mateix temps, el proc��s de presa de decisions mostra de forma objectiva, transparent i sistem��tica el perqu�� una alternativa ��s seleccionada en front de les altres, proporcionant l'opci�� que m��s b�� acompleix els objectius marcats, mostrant els punts forts i febles, les principals correlacions entre objectius i alternatives, i finalment tenint en compte la possible incertesa inherent en els par��metres del model que es fan servir durant les an��lisis. Les possibilitats del m��tode desenvolupat es demostren en aquesta tesi a partir de diferents casos d'estudi: selecci�� del tipus d'eliminaci�� biol��gica de nitrogen (cas d'estudi # 1), optimitzaci�� d'una estrat��gia de control (cas d'estudi # 2), redisseny d'una planta per aconseguir eliminaci�� simult��nia de carboni, nitrogen i f��sfor (cas d'estudi # 3) i finalment an��lisi d'estrat��gies control a nivell de planta (casos d'estudi # 4 i # 5).

Onset of recent rapid sea-level rise in the western Atlantic Ocean

A high-resolution record of sea-level change spanning the past 1000 years is derived from foraminiferal and chronological analyses of a 2m thick salt-marsh peat sequence at Chezzetcook, Nova Scotia, Canada. Former mean tide level positions are reconstructed with a precision of +/- 0.055 in using a transfer function derived from distributions of modern salt-marsh foraminifera. Our age model for the core section older than 300 years is based on 19 AMS C-14 ages and takes into account the individual probability distributions of calibrated radiocarbon ages. The past 300 years is dated by pollen and the isotopes Pb-206, Pb-207, Pb-210, Cs-137 and Am-241. Between AD 1000 and AD 1800, relative sea level rose at a mean rate of 17cm per century. Apparent pre-industrial rises of sea level dated at AD 1500-1550 and AD 1700-1800 cannot be clearly distinguished when radiocarbon age errors are taken into account. Furthermore, they may be an artefact of fluctuations in atmospheric C-14 production. In the 19th century sea level rose at a mean rate of 1.6mm/yr. Between AD 1900 and AD 1920, sea-level rise accelerated to the modern mean rate of 3.2mm/yr. This acceleration corresponds in time with global temperature rise and may therefore be associated with recent global warming. (c) 2005 Elsevier Ltd. All rights reserved.

Impacts of climate change scenarios on dissolved oxygen in the River Thames, UK

A water quality model is used to assess the impact of possible climate change on dissolved oxygen (DO) in the Thames. The Thames catchment is densely populated and, typically, many pressures are anthropogenic. However, that same population also relies on the river for potable water supply and as a disposal route for treated wastewater. Thus, future water quality will be highly dependent on future activity. Dynamic and stochastic modelling has been used to assess the likely impacts on DO dynamics along the river system and the probability distributions associated with future variability. The modelling predictions indicate that warmer river temperatures and drought act to reduce dissolved oxygen concentrations in lowland river systems

Global observed changes in daily climate extremes of temperature and precipitation

A suite of climate change indices derived from daily temperature and precipitation data, with a primary focus on extreme events, were computed and analyzed. By setting an exact formula for each index and using specially designed software, analyses done in different countries have been combined seamlessly. This has enabled the presentation of the most up-to-date and comprehensive global picture of trends in extreme temperature and precipitation indices using results from a number of workshops held in data-sparse regions and high-quality station data supplied by numerous scientists world wide. Seasonal and annual indices for the period 1951-2003 were gridded. Trends in the gridded fields were computed and tested for statistical significance. Results showed widespread significant changes in temperature extremes associated with warming, especially for those indices derived from daily minimum temperature. Over 70% of the global land area sampled showed a significant decrease in the annual occurrence of cold nights and a significant increase in the annual occurrence of warm nights. Some regions experienced a more than doubling of these indices. This implies a positive shift in the distribution of daily minimum temperature throughout the globe. Daily maximum temperature indices showed similar changes but with smaller magnitudes. Precipitation changes showed a widespread and significant increase, but the changes are much less spatially coherent compared with temperature change. Probability distributions of indices derived from approximately 200 temperature and 600 precipitation stations, with near-complete data for 1901-2003 and covering a very large region of the Northern Hemisphere midlatitudes (and parts of Australia for precipitation) were analyzed for the periods 1901-1950, 1951-1978 and 1979-2003. Results indicate a significant warming throughout the 20th century. Differences in temperature indices distributions are particularly pronounced between the most recent two periods and for those indices related to minimum temperature. An analysis of those indices for which seasonal time series are available shows that these changes occur for all seasons although they are generally least pronounced for September to November. Precipitation indices show a tendency toward wetter conditions throughout the 20th century.

A systematic review of the routine monitoring of growth in children of primary school age to identify growth-related conditions

Objectives: To clarify the role of growth monitoring in primary school children, including obesity, and to examine issues that might impact on the effectiveness and cost-effectiveness of such programmes. Data sources: Electronic databases were searched up to July 2005. Experts in the field were also consulted. Review methods: Data extraction and quality assessment were performed on studies meeting the review's inclusion criteria. The performance of growth monitoring to detect disorders of stature and obesity was evaluated against National Screening Committee (NSC) criteria. Results: In the 31 studies that were included in the review, there were no controlled trials of the impact of growth monitoring and no studies of the diagnostic accuracy of different methods for growth monitoring. Analysis of the studies that presented a 'diagnostic yield' of growth monitoring suggested that one-off screening might identify between 1: 545 and 1: 1793 new cases of potentially treatable conditions. Economic modelling suggested that growth monitoring is associated with health improvements [ incremental cost per quality-adjusted life-year (QALY) of pound 9500] and indicated that monitoring was cost-effective 100% of the time over the given probability distributions for a willingness to pay threshold of pound 30,000 per QALY. Studies of obesity focused on the performance of body mass index against measures of body fat. A number of issues relating to human resources required for growth monitoring were identified, but data on attitudes to growth monitoring were extremely sparse. Preliminary findings from economic modelling suggested that primary prevention may be the most cost-effective approach to obesity management, but the model incorporated a great deal of uncertainty. Conclusions: This review has indicated the potential utility and cost-effectiveness of growth monitoring in terms of increased detection of stature-related disorders. It has also pointed strongly to the need for further research. Growth monitoring does not currently meet all NSC criteria. However, it is questionable whether some of these criteria can be meaningfully applied to growth monitoring given that short stature is not a disease in itself, but is used as a marker for a range of pathologies and as an indicator of general health status. Identification of effective interventions for the treatment of obesity is likely to be considered a prerequisite to any move from monitoring to a screening programme designed to identify individual overweight and obese children. Similarly, further long-term studies of the predictors of obesity-related co-morbidities in adulthood are warranted. A cluster randomised trial comparing growth monitoring strategies with no growth monitoring in the general population would most reliably determine the clinical effectiveness of growth monitoring. Studies of diagnostic accuracy, alongside evidence of effective treatment strategies, could provide an alternative approach. In this context, careful consideration would need to be given to target conditions and intervention thresholds. Diagnostic accuracy studies would require long-term follow-up of both short and normal children to determine sensitivity and specificity of growth monitoring.

Measuring gametic disequilibrium from multilocus data

We describe a Bayesian approach to analyzing multilocus genotype or haplotype data to assess departures from gametic (linkage) equilibrium. Our approach employs a Markov chain Monte Carlo (MCMC) algorithm to approximate the posterior probability distributions of disequilibrium parameters. The distributions are computed exactly in some simple settings. Among other advantages, posterior distributions can be presented visually, which allows the uncertainties in parameter estimates to be readily assessed. In addition, background knowledge can be incorporated, where available, to improve the precision of inferences. The method is illustrated by application to previously published datasets; implications for multilocus forensic match probabilities and for simple association-based gene mapping are also discussed.

Decision theory and real estate development: a note on uncertainty

Real estate development appraisal is a quantification of future expectations. The appraisal model relies upon the valuer/developer having an understanding of the future in terms of the future marketability of the completed development and the future cost of development. In some cases the developer has some degree of control over the possible variation in the variables, as with the cost of construction through the choice of specification. However, other variables, such as the sale price of the final product, are totally dependent upon the vagaries of the market at the completion date. To try to address the risk of a different outcome to the one expected (modelled) the developer will often carry out a sensitivity analysis on the development. However, traditional sensitivity analysis has generally only looked at the best and worst scenarios and has focused on the anticipated or expected outcomes. This does not take into account uncertainty and the range of outcomes that can happen. A fuller analysis should include examination of the uncertainties in each of the components of the appraisal and account for the appropriate distributions of the variables. Similarly, as many of the variables in the model are not independent, the variables need to be correlated. This requires a standardised approach and we suggest that the use of a generic forecasting software package, in this case Crystal Ball, allows the analyst to work with an existing development appraisal model set up in Excel (or other spreadsheet) and to work with a predetermined set of probability distributions. Without a full knowledge of risk, developers are unable to determine the anticipated level of return that should be sought to compensate for the risk. This model allows the user a better understanding of the possible outcomes for the development. Ultimately the final decision will be made relative to current expectations and current business constraints, but by assessing the upside and downside risks more appropriately, the decision maker should be better placed to make a more informed and ���better���.

Three dimensional picture of the local structure of 1,4-Polybutadiene from a complete atomistic model and neutron scattering data

An efficient method of combining neutron diffraction data over an extended Q range with detailed atomistic models is presented. A quantitative and qualitative mapping of the organization of the chain conformation in both glass and liquid phase has been performed. The proposed structural refinement method is based on the exploitation of the intrachain features of the diffraction pattern by the use of internal coordinates for bond lengths, valence angles and torsion rotations. Models are built stochastically by assignment of these internal coordinates from probability distributions with limited variable parameters. Variation of these parameters is used in the construction of models that minimize the differences between the observed and calculated structure factors. A series of neutron scattering data of 1,4-polybutadiene at the region 20320 K is presented. Analysis of the experimental data yield bond lengths for C-C and C=C of 1.54 and 1.35 �� respectively. Valence angles of the backbone were found to be at 112 and 122.8 for the CCC and CC=C respectively. Three torsion angles corresponding to the double bond and the adjacent R and �� bonds were found to occupy cis and trans, s(, trans and g( and trans states, respectively. We compare our results with theoretical predictions, computer simulations, RIS models, and previously reported experimental results.

Fuzzy analysis: a vague way of dealing with uncertainty in real estate analysis?

Risk and uncertainty are, to say the least, poorly considered by most individuals involved in real estate analysis - in both development and investment appraisal. Surveyors continue to express 'uncertainty' about the value (risk) of using relatively objective methods of analysis to account for these factors. These methods attempt to identify the risk elements more explicitly. Conventionally this is done by deriving probability distributions for the uncontrolled variables in the system. A suggested 'new' way of "being able to express our uncertainty or slight vagueness about some of the qualitative judgements and not entirely certain data required in the course of the problem..." uses the application of fuzzy logic. This paper discusses and demonstrates the terminology and methodology of fuzzy analysis. In particular it attempts a comparison of the procedures with those used in 'conventional' risk analysis approaches and critically investigates whether a fuzzy approach offers an alternative to the use of probability based analysis for dealing with aspects of risk and uncertainty in real estate analysis