Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 172

Search results for: ruin probabilities

172 Quality of the Ruin Probabilities Approximation Using the Regenerative Processes Approach regarding to Large Claims

Authors: Safia Hocine, Djamil Aïssani

Abstract:

Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: heavy-tailed distribution, large claims, regenerative process, risk model, ruin probability, stability

Procedia PDF Downloads 276
171 A Hazard Rate Function for the Time of Ruin

Authors: Sule Sahin, Basak Bulut Karageyik

Abstract:

This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

Procedia PDF Downloads 227
170 A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes

Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

Procedia PDF Downloads 200
169 Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model

Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

Procedia PDF Downloads 177
168 Quantum Mechanics Approach for Ruin Probability

Authors: Ahmet Kaya

Abstract:

Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

Procedia PDF Downloads 248
167 Quantum Mechanism Approach for Non-Ruin Probability and Comparison of Path Integral Method and Stochastic Simulations

Authors: Ahmet Kaya

Abstract:

Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

Procedia PDF Downloads 192
166 Generalized Extreme Value Regression with Binary Dependent Variable: An Application for Predicting Meteorological Drought Probabilities

Authors: Retius Chifurira

Abstract:

Logistic regression model is the most used regression model to predict meteorological drought probabilities. When the dependent variable is extreme, the logistic model fails to adequately capture drought probabilities. In order to adequately predict drought probabilities, we use the generalized linear model (GLM) with the quantile function of the generalized extreme value distribution (GEVD) as the link function. The method maximum likelihood estimation is used to estimate the parameters of the generalized extreme value (GEV) regression model. We compare the performance of the logistic and the GEV regression models in predicting drought probabilities for Zimbabwe. The performance of the regression models are assessed using the goodness-of-fit tests, namely; relative root mean square error (RRMSE) and relative mean absolute error (RMAE). Results show that the GEV regression model performs better than the logistic model, thereby providing a good alternative candidate for predicting drought probabilities. This paper provides the first application of GLM derived from extreme value theory to predict drought probabilities for a drought-prone country such as Zimbabwe.

Keywords: generalized extreme value distribution, general linear model, mean annual rainfall, meteorological drought probabilities

Procedia PDF Downloads 102
165 Equity Investment Restrictions and Pension Replacement Rates in Nigeria: A Ruin-Risk Analysis

Authors: Uche A. Ibekwe

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Pension funds are pooled assets which are established to provide income for retirees. The funds are usually regulated to check excessive risk taking by fund managers. In Nigeria, the current defined contribution (DC) pension scheme appears to contain some overly stringent restrictions which might be hampering its successful implementation. Notable among these restrictions is the 25 percent maximum limit on investment in ordinary shares of quoted companies. This paper examines the extent to which these restrictions affect pension replacement rates at retirement. The study made use of both simulated and historical asset return distributions using mean-variance, regression analysis and ruin-risk analyses, the study found that the current equity investment restriction policy in Nigeria reduces replacement rates at retirement.

Keywords: equity investment, replacement rates, restrictions, ruin-risk

Procedia PDF Downloads 271
164 A Study of Life Expectancy in an Urban Set up of North-Eastern India under Dynamic Consideration Incorporating Cause Specific Mortality

Authors: Mompi Sharma, Labananda Choudhury, Anjana M. Saikia

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Background: The period life table is entirely based on the assumption that the mortality patterns of the population existing in the given period will persist throughout their lives. However, it has been observed that the mortality rate continues to decline. As such, if the rates of change of probabilities of death are considered in a life table then we get a dynamic life table. Although, mortality has been declining in all parts of India, one may be interested to know whether these declines had appeared more in an urban area of underdeveloped regions like North-Eastern India. So, attempt has been made to know the mortality pattern and the life expectancy under dynamic scenario in Guwahati, the biggest city of North Eastern India. Further, if the probabilities of death changes then there is a possibility that its different constituent probabilities will also change. Since cardiovascular disease (CVD) is the leading cause of death in Guwahati. Therefore, an attempt has also been made to formulate dynamic cause specific death ratio and probabilities of death due to CVD. Objectives: To construct dynamic life table for Guwahati for the year 2011 based on the rates of change of probabilities of death over the previous 10 and 25 years (i.e.,2001 and 1986) and to compute corresponding dynamic cause specific death ratio and probabilities of death due to CVD. Methodology and Data: The study uses the method proposed by Denton and Spencer (2011) to construct dynamic life table for Guwahati. So, the data from the Office of the Birth and Death, Guwahati Municipal Corporation for the years 1986, 2001 and 2011 are taken. The population based data are taken from 2001 and 2011 census (India). However, the population data for 1986 has been estimated. Also, the cause of death ratio and probabilities of death due to CVD are computed for the aforementioned years and then extended to dynamic set up for the year 2011 by considering the rates of change of those probabilities over the previous 10 and 25 years. Findings: The dynamic life expectancy at birth (LEB) for Guwahati is found to be higher than the corresponding values in the period table by 3.28 (5.65) years for males and 8.30 (6.37) years for females during the period of 10 (25) years. The life expectancies under dynamic consideration in all the other age groups are also seen higher than the usual life expectancies, which may be possible due to gradual decline in probabilities of death since 1986-2011. Further, a continuous decline has also been observed in death ratio due to CVD along with cause specific probabilities of death for both sexes. As a consequence, dynamic cause of death probability due to CVD is found to be less in comparison to usual procedure. Conclusion: Since incorporation of changing mortality rates in period life table for Guwahati resulted in higher life expectancies and lower probabilities of death due to CVD, this would possibly bring out the real situation of deaths prevailing in the city.

Keywords: cause specific death ratio, cause specific probabilities of death, dynamic, life expectancy

Procedia PDF Downloads 162
163 Critical Appraisal of Different Drought Indices of Drought Predection and Their Application in KBK Districts of Odisha

Authors: Bibhuti Bhusan Sahoo, Ramakar Jha

Abstract:

Mapping of the extreme events (droughts) is one of the adaptation strategies to consequences of increasing climatic inconsistency and climate alterations. There is no operational practice to forecast the drought. One of the suggestions is to update mapping of drought prone areas for developmental planning. Drought indices play a significant role in drought mitigation. Many scientists have worked on different statistical analysis in drought and other climatological hazards. Many researchers have studied droughts individually for different sub-divisions or for India. Very few workers have studied district wise probabilities over large scale. In the present study, district wise drought probabilities over KBK (Kalahandi-Balangir-Koraput) districts of Odisha, India, Which are seriously prone to droughts, has been established using Hydrological drought index and Meteorological drought index along with the remote sensing drought indices to develop a multidirectional approach in the field of drought mitigation. Mapping for moderate and severe drought probabilities for KBK districts has been done and regions belonging different class intervals of probabilities of drought have been demarcated. Such type of information would be a good tool for planning purposes, for input in modelling and better promising results can be achieved.

Keywords: drought indices, KBK districts, proposed drought severity index, SPI

Procedia PDF Downloads 357
162 Calculating Collision Risk Exposures and Risk Probabilities at Container Terminals

Authors: Mohammad Ali Hasanzadeh, Thierry Vanelslander, Eddy Van De Voorde

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Nowadays maritime transport is a key element in international trade and global supply chain. Economies of scale in transporting goods are one of the most attractive elements of using ships. Without maritime transport, almost no globalization of economics can be imagined. Within maritime transport, ports are the interface between lands and see. Even though using ships help cargo owners to have a competitive margin but an accident in port during loading or unloading or even moving cargoes within the terminal can diminish such margin. Statistics shows that due to the high-speed notion of activities within ports, collision accidents are the most common type of accidents. To mitigate such accidents, the appropriate risk exposures have to be defined and calculate, later on risk probabilities can be determined for each type of accident, i.e. fatal, severe, moderate and minor ones. Having such risk probabilities help managers to define the effectiveness of each collision risk control option. This research defined travelled distance as main collision risk exposure in container terminals, taking all the related items into consideration, it was calculated for Shahid Rajae container terminals. Following this finding, collision risk probabilities were computed.

Keywords: collision accident, container terminal, maritime transport, risk exposure

Procedia PDF Downloads 283
161 Modeling Binomial Dependent Distribution of the Values: Synthesis Tables of Probabilities of Errors of the First and Second Kind of Biometrics-Neural Network Authentication System

Authors: B. S.Akhmetov, S. T. Akhmetova, D. N. Nadeyev, V. Yu. Yegorov, V. V. Smogoonov

Abstract:

Estimated probabilities of errors of the first and second kind for nonideal biometrics-neural transducers 256 outputs, the construction of nomograms based error probability of 'own' and 'alien' from the mathematical expectation and standard deviation of the normalized measures Hamming.

Keywords: modeling, errors, probability, biometrics, neural network, authentication

Procedia PDF Downloads 412
160 Factorization of Computations in Bayesian Networks: Interpretation of Factors

Authors: Linda Smail, Zineb Azouz

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Given a Bayesian network relative to a set I of discrete random variables, we are interested in computing the probability distribution P(S) where S is a subset of I. The general idea is to write the expression of P(S) in the form of a product of factors where each factor is easy to compute. More importantly, it will be very useful to give an interpretation of each of the factors in terms of conditional probabilities. This paper considers a semantic interpretation of the factors involved in computing marginal probabilities in Bayesian networks. Establishing such a semantic interpretations is indeed interesting and relevant in the case of large Bayesian networks.

Keywords: Bayesian networks, D-Separation, level two Bayesian networks, factorization of computation

Procedia PDF Downloads 426
159 Logistic Regression Model versus Additive Model for Recurrent Event Data

Authors: Entisar A. Elgmati

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Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

Procedia PDF Downloads 515
158 Semi-Supervised Learning Using Pseudo F Measure

Authors: Mahesh Balan U, Rohith Srinivaas Mohanakrishnan, Venkat Subramanian

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Positive and unlabeled learning (PU) has gained more attention in both academic and industry research literature recently because of its relevance to existing business problems today. Yet, there still seems to be some existing challenges in terms of validating the performance of PU learning, as the actual truth of unlabeled data points is still unknown in contrast to a binary classification where we know the truth. In this study, we propose a novel PU learning technique based on the Pseudo-F measure, where we address this research gap. In this approach, we train the PU model to discriminate the probability distribution of the positive and unlabeled in the validation and spy data. The predicted probabilities of the PU model have a two-fold validation – (a) the predicted probabilities of reliable positives and predicted positives should be from the same distribution; (b) the predicted probabilities of predicted positives and predicted unlabeled should be from a different distribution. We experimented with this approach on a credit marketing case study in one of the world’s biggest fintech platforms and found evidence for benchmarking performance and backtested using historical data. This study contributes to the existing literature on semi-supervised learning.

Keywords: PU learning, semi-supervised learning, pseudo f measure, classification

Procedia PDF Downloads 98
157 Determinants of Probability Weighting and Probability Neglect: An Experimental Study of the Role of Emotions, Risk Perception, and Personality in Flood Insurance Demand

Authors: Peter J. Robinson, W. J. Wouter Botzen

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Individuals often over-weight low probabilities and under-weight moderate to high probabilities, however very low probabilities are either significantly over-weighted or neglected. Little is known about factors affecting probability weighting in Prospect Theory related to emotions specific to risk (anticipatory and anticipated emotions), the threshold of concern, as well as personality traits like locus of control. This study provides these insights by examining factors that influence probability weighting in the context of flood insurance demand in an economic experiment. In particular, we focus on determinants of flood probability neglect to provide recommendations for improved risk management. In addition, results obtained using real incentives and no performance-based payments are compared in the experiment with high experimental outcomes. Based on data collected from 1’041 Dutch homeowners, we find that: flood probability neglect is related to anticipated regret, worry and the threshold of concern. Moreover, locus of control and regret affect probabilistic pessimism. Nevertheless, we do not observe strong evidence that incentives influence flood probability neglect nor probability weighting. The results show that low, moderate and high flood probabilities are under-weighted, which is related to framing in the flooding context and the degree of realism respondents attach to high probability property damages. We suggest several policies to overcome psychological factors related to under-weighting flood probabilities to improve flood preparations. These include policies that promote better risk communication to enhance insurance decisions for individuals with a high threshold of concern, and education and information provision to change the behaviour of internal locus of control types as well as people who see insurance as an investment. Multi-year flood insurance may also prevent short-sighted behaviour of people who have a tendency to regret paying for insurance. Moreover, bundling low-probability/high-impact risks with more immediate risks may achieve an overall covered risk which is less likely to be judged as falling below thresholds of concern. These measures could aid the development of a flood insurance market in the Netherlands for which we find to be demand.

Keywords: flood insurance demand, prospect theory, risk perceptions, risk preferences

Procedia PDF Downloads 203
156 Decision-Making Under Uncertainty in Obsessive-Compulsive Disorder

Authors: Helen Pushkarskaya, David Tolin, Lital Ruderman, Ariel Kirshenbaum, J. MacLaren Kelly, Christopher Pittenger, Ifat Levy

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Obsessive-Compulsive Disorder (OCD) produces profound morbidity. Difficulties with decision making and intolerance of uncertainty are prominent clinical features of OCD. The nature and etiology of these deficits are poorly understood. We used a well-validated choice task, grounded in behavioral economic theory, to investigate differences in valuation and value-based choice during decision making under uncertainty in 20 unmedicated participants with OCD and 20 matched healthy controls. Participants’ choices were used to assess individual decision-making characteristics. Compared to controls, individuals with OCD were less consistent in their choices and less able to identify options that were unambiguously preferable. These differences correlated with symptom severity. OCD participants did not differ from controls in how they valued uncertain options when outcome probabilities were known (risk) but were more likely than controls to avoid uncertain options when these probabilities were imprecisely specified (ambiguity). These results suggest that the underlying neural mechanisms of valuation and value-based choices during decision-making are abnormal in OCD. Individuals with OCD show elevated intolerance of uncertainty, but only when outcome probabilities are themselves uncertain. Future research focused on the neural valuation network, which is implicated in value-based computations, may provide new neurocognitive insights into the pathophysiology of OCD. Deficits in decision-making processes may represent a target for therapeutic intervention.

Keywords: obsessive compulsive disorder, decision-making, uncertainty intolerance, risk aversion, ambiguity aversion, valuation

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155 Optical Emission Studies of Laser Produced Lead Plasma: Measurements of Transition Probabilities of the 6P7S → 6P2 Transitions Array

Authors: Javed Iqbal, R. Ahmed, M. A. Baig

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We present new data on the optical emission spectra of the laser produced lead plasma using a pulsed Nd:YAG laser at 1064 nm (pulse energy 400 mJ, pulse width 5 ns, 10 Hz repetition rate) in conjunction with a set of miniature spectrometers covering the spectral range from 200 nm to 720 nm. Well resolved structure due to the 6p7s → 6p2 transition array of neutral lead and a few multiplets of singly ionized lead have been observed. The electron temperatures have been calculated in the range (9000 - 10800) ± 500 K using four methods; two line ratio, Boltzmann plot, Saha-Boltzmann plot and Morrata method whereas, the electron number densities have been determined in the range (2.0 – 8.0) ± 0.6 ×1016 cm-3 using the Stark broadened line profiles of neutral lead lines, singly ionized lead lines and hydrogen Hα-line. Full width at half maximum (FWHM) of a number of neutral and singly ionized lead lines have been extracted by the Lorentzian fit to the experimentally observed line profiles. Furthermore, branching fractions have been deduced for eleven lines of the 6p7s → 6p2 transition array in lead whereas the absolute values of the transition probabilities have been calculated by combining the experimental branching fractions with the life times of the excited levels The new results are compared with the existing data showing a good agreement.

Keywords: LIBS, plasma parameters, transition probabilities, branching fractions, stark width

Procedia PDF Downloads 211
154 Churn Prediction for Telecommunication Industry Using Artificial Neural Networks

Authors: Ulas Vural, M. Ergun Okay, E. Mesut Yildiz

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Telecommunication service providers demand accurate and precise prediction of customer churn probabilities to increase the effectiveness of their customer relation services. The large amount of customer data owned by the service providers is suitable for analysis by machine learning methods. In this study, expenditure data of customers are analyzed by using an artificial neural network (ANN). The ANN model is applied to the data of customers with different billing duration. The proposed model successfully predicts the churn probabilities at 83% accuracy for only three months expenditure data and the prediction accuracy increases up to 89% when the nine month data is used. The experiments also show that the accuracy of ANN model increases on an extended feature set with information of the changes on the bill amounts.

Keywords: customer relationship management, churn prediction, telecom industry, deep learning, artificial neural networks

Procedia PDF Downloads 76
153 Degradation Model for UK Railway Drainage System

Authors: Yiqi Wu, Simon Tait, Andrew Nichols

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Management of UK railway drainage assets is challenging due to the large amounts of historical assets with long asset life cycles. A major concern for asset managers is to maintain the required performance economically and efficiently while complying with the relevant regulation and legislation. As the majority of the drainage assets are buried underground and are often difficult or costly to examine, it is important for asset managers to understand and model the degradation process in order to foresee the upcoming reduction in asset performance and conduct proactive maintenance accordingly. In this research, a Markov chain approach is used to model the deterioration process of rail drainage assets. The study is based on historical condition scores and characteristics of drainage assets across the whole railway network in England, Scotland, and Wales. The model is used to examine the effect of various characteristics on the probabilities of degradation, for example, the regional difference in probabilities of degradation, and how material and shape can influence the deterioration process for chambers, channels, and pipes.

Keywords: deterioration, degradation, markov models, probability, railway drainage

Procedia PDF Downloads 101
152 Neural Correlates of Decision-Making Under Ambiguity and Conflict

Authors: Helen Pushkarskaya, Michael Smithson, Jane E. Joseph, Christine Corbly, Ifat Levy

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Studies of decision making under uncertainty generally focus on imprecise information about outcome probabilities (“ambiguity”). It is not clear, however, whether conflicting information about outcome probabilities affects decision making in the same manner as ambiguity does. Here we combine functional Magnetic Resonance Imaging (fMRI) and a simple gamble design to study this question. In this design, the levels of ambiguity and conflict are parametrically varied, and ambiguity and conflict gambles are matched on both expected value and variance. Behaviorally, participants avoided conflict more than ambiguity, and attitudes toward ambiguity and conflict did not correlate across subjects. Neurally, regional brain activation was differentially modulated by ambiguity level and aversion to ambiguity and by conflict level and aversion to conflict. Activation in the medial prefrontal cortex was correlated with the level of ambiguity and with ambiguity aversion, whereas activation in the ventral striatum was correlated with the level of conflict and with conflict aversion. This novel double dissociation indicates that decision makers process imprecise and conflicting information differently, a finding that has important implications for basic and clinical research.

Keywords: decision making, uncertainty, ambiguity, conflict, fMRI

Procedia PDF Downloads 443
151 Life Cycle Cost Evaluation of Structures with Hysteretic Dampers

Authors: Jinkoo Kim, Hyungoo Kang, Hyungjun Shin

Abstract:

In this study, a hybrid energy dissipation device is developed by combining a steel slit plate and friction pads to be used for seismic retrofit of structures, and its effectiveness is investigated by comparing the life cycle costs of the structure before and after the retrofit. The seismic energy dissipation capability of the dampers is confirmed by cyclic loading tests. The probabilities of reaching various damage states are obtained by fragility analysis, and the life cycle costs of the model structures are computed using the PACT (Performance Assessment Calculation Tool) program based on FEMA P-58 methodology. The fragility analysis shows that the probabilities of reaching limit states are minimized by the seismic retrofit with hybrid dampers and increasing column size. The seismic retrofit with increasing column size and hybrid dampers results in the lowest repair cost and shortest repair time.

Keywords: slit dampers, friction dampers, seismic retrofit, life cycle cost, FEMA P-58, PACT

Procedia PDF Downloads 259
150 Controlling the Expense of Political Contests Using a Modified N-Players Tullock’s Model

Authors: C. Cohen, O. Levi

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This work introduces a generalization of the classical Tullock’s model of one-stage contests under complete information with multiple unlimited numbers of contestants. In classical Tullock’s model, the contest winner is not necessarily the highest bidder. Instead, the winner is determined according to a draw in which the winning probabilities are the relative contestants’ efforts. The Tullock modeling fits well political contests, in which the winner is not necessarily the highest effort contestant. This work presents a modified model which uses a simple non-discriminating rule, namely, a parameter to influence the total costs planned for an election, for example, the contest designer can control the contestants' efforts. The winner pays a fee, and the losers are reimbursed the same amount. Our proposed model includes a mechanism that controls the efforts exerted and balances competition, creating a tighter, less predictable and more interesting contest. Additionally, the proposed model follows the fairness criterion in the sense that it does not alter the contestants' probabilities of winning compared to the classic Tullock’s model. We provide an analytic solution for the contestant's optimal effort and expected reward.

Keywords: contests, Tullock's model, political elections, control expenses

Procedia PDF Downloads 65
149 Use of Multistage Transition Regression Models for Credit Card Income Prediction

Authors: Denys Osipenko, Jonathan Crook

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Because of the variety of the card holders’ behaviour types and income sources each consumer account can be transferred to a variety of states. Each consumer account can be inactive, transactor, revolver, delinquent, defaulted and requires an individual model for the income prediction. The estimation of transition probabilities between statuses at the account level helps to avoid the memorylessness of the Markov Chains approach. This paper investigates the transition probabilities estimation approaches to credit cards income prediction at the account level. The key question of empirical research is which approach gives more accurate results: multinomial logistic regression or multistage conditional logistic regression with binary target. Both models have shown moderate predictive power. Prediction accuracy for conditional logistic regression depends on the order of stages for the conditional binary logistic regression. On the other hand, multinomial logistic regression is easier for usage and gives integrate estimations for all states without priorities. Thus further investigations can be concentrated on alternative modeling approaches such as discrete choice models.

Keywords: multinomial regression, conditional logistic regression, credit account state, transition probability

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148 Applied Complement of Probability and Information Entropy for Prediction in Student Learning

Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

Procedia PDF Downloads 75
147 Binary Decision Diagram Based Methods to Evaluate the Reliability of Systems Considering Failure Dependencies

Authors: Siqi Qiu, Yijian Zheng, Xin Guo Ming

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In many reliability and risk analysis, failures of components are supposed to be independent. However, in reality, the ignorance of failure dependencies among components may render the results of reliability and risk analysis incorrect. There are two principal ways to incorporate failure dependencies in system reliability and risk analysis: implicit and explicit methods. In the implicit method, failure dependencies can be modeled by joint probabilities, correlation values or conditional probabilities. In the explicit method, certain types of dependencies can be modeled in a fault tree as mutually independent basic events for specific component failures. In this paper, explicit and implicit methods based on BDD will be proposed to evaluate the reliability of systems considering failure dependencies. The obtained results prove the equivalence of the proposed implicit and explicit methods. It is found that the consideration of failure dependencies decreases the reliability of systems. This observation is intuitive, because more components fail due to failure dependencies. The consideration of failure dependencies helps designers to reduce the dependencies between components during the design phase to make the system more reliable.

Keywords: reliability assessment, risk assessment, failure dependencies, binary decision diagram

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146 Seismic Performance Evaluation of Structures with Hybrid Dampers Based on FEMA P-58 Methodology

Authors: Minsung Kim, Hyunkoo Kang, Jinkoo Kim

Abstract:

In this study, a hybrid energy dissipation device is developed by combining a steel slit plate and friction pads to be used for seismic retrofit of structures, and its effectiveness is investigated by comparing the life cycle costs of the structure before and after the retrofit. The seismic energy dissipation capability of the dampers is confirmed by cyclic loading tests. The probabilities of reaching various damage states are obtained by fragility analysis, and the life cycle costs of the model structures are computed using the PACT (Performance Assessment Calculation Tool) program based on FEMA P-58 methodology. The fragility analysis shows that the probabilities of reaching limit states are minimized by the seismic retrofit with hybrid dampers and increasing column size. The seismic retrofit with increasing column size and hybrid dampers results in the lowest repair cost and shortest repair time. This research was supported by a grant (13AUDP-B066083-01) from Architecture & Urban Development Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.

Keywords: FEMA P-58, friction dampers, life cycle cost, seismic retrofit

Procedia PDF Downloads 243
145 A Generalization of Planar Pascal’s Triangle to Polynomial Expansion and Connection with Sierpinski Patterns

Authors: Wajdi Mohamed Ratemi

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The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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144 Estimating Bridge Deterioration for Small Data Sets Using Regression and Markov Models

Authors: Yina F. Muñoz, Alexander Paz, Hanns De La Fuente-Mella, Joaquin V. Fariña, Guilherme M. Sales

Abstract:

The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.

Keywords: concrete bridges, deterioration, Markov chains, probability matrix

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143 Investigating Mathematical Knowledge of Teaching for Secondary Preservice Teachers in Papua New Guinea Based on Probabilities

Authors: Murray Olowa

Abstract:

This article examines the studies investigating the Mathematical Knowledge for Teaching (MKT) of secondary preservice teachers in Papua New Guinea based on probabilities. The study was carried out with the support of previous research on Pedagogical Content Knowledge (PCK) and Subject Matter Knowledge (SMK). This research was conducted due to the continuous issues faced in the country in both primary and secondary education, like changes in curriculum, emphasis on mathematics and science education, and a decline in mathematics performance. Moreover, the mathematics curriculum doesn’t capture PCK or SMK. The two main domains that have been identified are SMK and PCK, which have been further sub-divided into Common Content Knowledge (CCK), Specialised Content Knowledge (SCK) and Horizon Content Knowledge (HCK), and Knowledge of Content and Students (KCS), Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), respectively. The data collected from 15-_year-_ ones and 15-_year-_fours conducted at St Peter Chanel Secondary Teachers College revealed that there is no significant difference in subject matter knowledge between year one and year four since the P-value of 0.22>0.05. However, it was revealed that year fours have higher pedagogical content knowledge than year one since P-value was 0.007<0.05. Finally, the research has proven that year fours have higher MKT than the year ones. This difference occurred due to final year preservice teachers’ hard work and engagement in mathematics curriculum and teaching practice.

Keywords: mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, Papua New Guinea, preservice teachers, probability

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