Search results for: probability distributions

Authors: Gubhinder Kundhi, Paul Rilstone

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It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: bootstrap, Instrumental Variable, Edgeworth expansions, Saddlepoint expansions

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Authors: M. R. Ghasemi, R. Ghiasi, H. Varaee

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Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.

Keywords: probability-based damage detection (PBDD), Kriging, surrogate modeling, uncertainty quantification, artificial intelligence, enhanced ideal gas molecular movement (EIGMM)

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Authors: D. Calogine, O. Chau, S. Dotti, O. Ramiarinjanahary, P. Rasoavonjy, F. Tovondahiniriko

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Mafate is a natural circus in the north-western part of Reunion Island, without an electrical grid and road network. A micro-grid concept is being experimented in this area, composed of a photovoltaic production combined with electrochemical batteries, in order to meet the local population for self-consumption of electricity demands. This work develops a discrete model as well as a stochastic model in order to reach an optimal equilibrium between production and consumptions for a cluster of houses. The management of the energy power leads to a large linearized programming system, where the time interval of interest is 24 hours The experimental data are solar production, storage energy, and the parameters of the different electrical devices and batteries. The unknown variables to evaluate are the consumptions of the various electrical services, the energy drawn from and stored in the batteries, and the inhabitants’ planning wishes. The objective is to fit the solar production to the electrical consumption of the inhabitants, with an optimal use of the energies in the batteries by satisfying as widely as possible the users' planning requirements. In the discrete model, the different parameters and solutions of the linear programming system are deterministic scalars. Whereas in the stochastic approach, the data parameters and the linear programming solutions become random variables, then the distributions of which could be imposed or established by estimation from samples of real observations or from samples of optimal discrete equilibrium solutions.

Keywords: photovoltaic production, power consumption, battery storage resources, random variables, stochastic modeling, estimations of probability distributions, mixed integer linear programming, smart micro-grid, self-consumption of electricity.

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Authors: K. A. Adepoju, O. I. Shittu, A. U. Chukwu

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In this paper, a new four-parameter generalized version of the Fisher Snedecor distribution called Beta- F distribution is introduced. The comprehensive account of the statistical properties of the new distributions was considered. Formal expressions for the cumulative density function, moments, moment generating function and maximum likelihood estimation, as well as its Fisher information, were obtained. The flexibility of this distribution as well as its robustness using cancer remission time data was demonstrated. The new distribution can be used in most applications where the assumption underlying the use of other lifetime distributions is violated.

Keywords: fisher-snedecor distribution, beta-f distribution, outlier, maximum likelihood method

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Authors: M. Sumida, T. Fujimoto

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Fiber-concentration distributions in pulp liquid flows behind dispersion promoters were experimentally investigated to explore the feasibility of improving operational performance of hydraulic headboxes in papermaking machines. The proposed research was performed in the form of a basic test conducted on a screen-type model comprising a circular cylinder inserted within a channel. Tests were performed using pulp liquid possessing fiber concentrations ranging from 0.3-1.0 wt% under different flow velocities of 0.016-0.74 m/s. Fiber-concentration distributions were measured using the transmitted light attenuation method. Obtained test results were analyzed, and the influence of the flow velocities on wake characteristics behind the cylinder has been investigated with reference to findings of our preceding studies concerning pulp liquid flows in straight channels. Changes in fiber-concentration distribution along the flow direction were observed to be substantially large in the section from the cylinder to four times its diameter downstream of its centerline. Findings of this study provide useful information concerning the development of hydraulic headboxes.

Keywords: dispersion promoter, fiber-concentration distribution, hydraulic headbox, pulp liquid flow

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Authors: Jialin Wu, Zhiwei Lian, Jieyu Tang, Jingyun Shen

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Tornado is a serious and unpredictable natural disaster, which has an important impact on people's production and life. The probability of being hit by tornadoes in China was analyzed considering the principles of tornado formation. Then some suggestions on layout and shapes for newly-built buildings were provided combined with the characteristics of tornado wind fields. Fuzzy clustering and inverse closeness methods were used to evaluate the probability levels of tornado risks in various provinces based on classification and ranking. GIS was adopted to display the results. Finally, wind field single-vortex tornado was studied to discuss the optimized design of rural low-rise houses in Yancheng, Jiangsu as an example. This paper may provide enough data to support building and urban design in some specific regions.

Keywords: tornado probability, computational fluid dynamics, fuzzy mathematics, optimal design

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Authors: Jian Huang, Weixin Qian, Haitao Zhang, Weiyong Ying

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Cobalt-gadolinium catalyst for Fischer-Tropsch synthesis was prepared by impregnation method with commercial silica gel, and its texture properties were characterized by BET, XRD, and TPR. The catalytic performance of the catalyst was tested in a fixed bed reactor. The results showed that the addition of gadolinium to the cobalt catalyst might decrease the size of cobalt particles, and increased the dispersion of catalytic active cobalt phases. The carbon number distributions for the catalysts was calculated by ASF equation.

Keywords: Fischer-Tropsch synthesis, cobalt-based catalysts, gadolinium, carbon number distributions

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Authors: Li Minghui, Min Shaorong, Zhang Jun

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This paper aims for studying the operational efficiency of surface warship’s motorized evasion to acoustic homing torpedo. It orderly developed trajectory model, self-guide detection model, vessel evasion model, as well as anti-torpedo error model in three-dimensional space to make up for the deficiency of precious researches analyzing two-dimensionally confrontational models. Then, making use of the Monte Carlo method, it carried out the simulation for the confrontation process of evasion in the environment of MATLAB. At last, it quantitatively analyzed the main factors which determine vessel’s survival probability. The results show that evasion relative bearing and speed will affect vessel’s survival probability significantly. Thus, choosing appropriate evasion relative bearing and speed according to alarming range and alarming relative bearing for torpedo, improving alarming range and positioning accuracy and reducing the response time against torpedo will improve the vessel’s survival probability significantly.

Keywords: acoustic homing torpedo, vessel evasion, monte carlo method, torpedo defense, vessel's survival probability

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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

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even though decreases at these extreme wind speeds but are not infinite. Moreover, we also found that it is possible to stabilize the power coefficient (stabilizing the output power) above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: probability, probability density function, stochastic, turbulence

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Authors: Aneia Rajiel Busmente, Renato Gunio Jr., Jazin Mautante, Denise Joy Mendoza, Raymond Benedict Tagorio, Gabriel Uy, Natalie Quinn Valenzuela, Ma. Elayza Villa, Francine Yezha Vizcarra, Sofia Madelle Yapan, Eugene Kurt Yboa

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COVID-19’s rapid spread caused a dramatic change in the nation, especially the educational system. The Department of Education was forced to adopt a practical learning platform without neglecting health, a printed modular distance learning. The Philippines' K–12 curriculum includes Statistics and Probability as one of the key courses as it offers students the knowledge to evaluate and comprehend data. Due to student’s difficulty and lack of understanding of the concepts of Statistics and Probability in Normal Distribution. The Self-Learning Module in Statistics and Probability about the Normal Distribution created by the Department of Education has several problems, including many activities, unclear illustrations, and insufficient examples of concepts which enables learners to have a difficulty accomplishing the module. The purpose of this study is to determine the effectiveness of self-learning module on the academic performance of students in the subject Statistics and Probability, it will also explore students’ perception towards the quality of created Self-Learning Module in Statistics and Probability. Despite the availability of Self-Learning Modules in Statistics and Probability in the Philippines, there are still few literatures that discuss its effectiveness in improving the performance of Senior High School students in Statistics and Probability. In this study, a Self-Learning Module on Normal Distribution is evaluated using a quasi-experimental design. STEM students in Grade 11 from National University's Nazareth School will be the study's participants, chosen by purposive sampling. Google Forms will be utilized to find at least 100 STEM students in Grade 11. The research instrument consists of 20-item pre- and post-test to assess participants' knowledge and performance regarding Normal Distribution, and a Likert scale survey to evaluate how the students perceived the self-learning module. Pre-test, post-test, and Likert scale surveys will be utilized to gather data, with Jeffreys' Amazing Statistics Program (JASP) software being used for analysis.

Keywords: self-learning module, academic performance, statistics and probability, normal distribution

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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

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

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we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Anshul Gupta, T. Shankar

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In this paper, we had analyzed the call drop to provide a good quality of service to user. By optimizing it we can increase the coverage area and also the reduction of interference and congestion created in a network. Basically handover is the transfer of call from one cell site to another site during a call. Here we have analyzed the whole network by two method-statistic model and analytic model. In statistic model we have collected all the data of a network during busy hour and normal 24 hours and in analytic model we have the equation through which we have to find the call drop probability. By avoiding unnecessary handovers we can increase the number of calls per hour. The most important parameter is co-efficient of variation on which the whole paper discussed.

Keywords: coefficient of variation, mean, standard deviation, call drop probability, handover

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Authors: Ayman Baklizi

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Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths.

Keywords: asymptotic intervals, Bayes intervals, bootstrap, generalized pivot variables, two-parameter exponential distribution, quantiles

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Authors: Margareth E. Bolla, Ludfi Djakfar, Achmad Wicaksono

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The increase in the number of motorcycle users in Indonesia is in line with the increase in accidents involving motorcycles. Several previous studies have shown that humans are the biggest factor causing accidents, and the driver's personality factor will affect his behavior on the road. This study was conducted to see how a person's personality traits will affect the probability of having an accident while driving. The Big Five Inventory (BFI) questionnaire and the Honda Riding Trainer (HRT) simulator were used as measuring tools, while the analysis carried out was logistic regression analysis. The results of the descriptive analysis of the respondent's personality based on the BFI show that the majority of drivers have the dominant character of neuroticism (34%), while the smallest group is the driver with the dominant type of openness character (6%). The percentage of motorists who were not involved in an accident was 54%. The results of the logistic regression analysis form a mathematical model as follows Y = -3.852 - 0.288 X1 + 0.596 X2 + 0.429 X3 - 0.386 X4 - 0.094 X5 + 0.436 X6 + 0.162 X7, where the results of hypothesis testing indicate that the variables openness, conscientiousness, extraversion, agreeableness, neuroticism, history of traffic accidents and age at starting driving did not have a significant effect on the probability of a motorcyclist being involved in an accident.

Keywords: accidents, BFI, probability, simulator

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Authors: Mustapha Kamel Mihoubi, Essadik Kerkar, Abdelhamid Hebbouche

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According to the randomness of most of the factors affecting the stability of a gravity dam, probability theory is generally used to TESTING the risk of failure and there is a confusing logical transition from the state of stability failed state, so the stability failure process is considered as a probable event. The control of risk of product failures is of capital importance for the control from a cross analysis of the gravity of the consequences and effects of the probability of occurrence of identified major accidents and can incur a significant risk to the concrete dam structures. Probabilistic risk analysis models are used to provide a better understanding the reliability and structural failure of the works, including when calculating stability of large structures to a major risk in the event of an accident or breakdown. This work is interested in the study of the probability of failure of concrete dams through the application of the reliability analysis methods including the methods used in engineering. It is in our case of the use of level II methods via the study limit state. Hence, the probability of product failures is estimated by analytical methods of the type FORM (First Order Reliability Method), SORM (Second Order Reliability Method). By way of comparison, a second level III method was used which generates a full analysis of the problem and involving an integration of the probability density function of, random variables are extended to the field of security by using of the method of Mont-Carlo simulations. Taking into account the change in stress following load combinations: normal, exceptional and extreme the acting on the dam, calculation results obtained have provided acceptable failure probability values which largely corroborate the theory, in fact, the probability of failure tends to increase with increasing load intensities thus causing a significant decrease in strength, especially in the presence of combinations of unique and extreme loads. Shear forces then induce a shift threatens the reliability of the structure by intolerable values of the probability of product failures. Especially, in case THE increase of uplift in a hypothetical default of the drainage system.

Keywords: dam, failure, limit state, monte-carlo, reliability, probability, sliding, Taylor

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Authors: Wing Kam Fung, Kexin Yu

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Child trafficking has been a serious problem in modern China. The Chinese government has established a national anti-trafficking DNA database to help reunite missing children with their families. The database collects DNA information from missing children's parents, trafficked and homeless children, then conducts paternity tests to find matched pairs. This paper considers the matching accuracy in such cases by looking into the exclusion probability in paternity testing. First, the situation of child trafficking in China is introduced. Next, derivations of the exclusion probability for both one-parent and two-parents cases are given, followed by extension to allow for 1 or 2 mutations. The accuracy of paternity testing of child trafficking cases is then assessed using the exclusion probabilities and available data. Finally, the number of loci that should be used to ensure a correct match is investigated.

Keywords: child trafficking, DNA database, exclusion probability, paternity testing

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Authors: M. Ranjeeth, S. Anuradha

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Spectrum sensing is the main feature of cognitive radio technology. Spectrum sensing gives an idea of detecting the presence of the primary users in a licensed spectrum. In this paper we compare the theoretical results of detection probability of different fading environments like Rayleigh, Rician, Nakagami-m fading channels with the simulation results using energy detection based spectrum sensing. The numerical results are plotted as P_f Vs P_d for different SNR values, fading parameters. It is observed that Nakagami fading channel performance is better than other fading channels by using energy detection in spectrum sensing. A MATLAB simulation test bench has been implemented to know the performance of energy detection in different fading channel environment.

Keywords: spectrum sensing, energy detection, fading channels, probability of detection, probability of false alarm

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

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A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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Authors: Abdelmounaim Zanaz, Sylvie Yotte, Fazia Fouchal, Alaa Chateauneuf

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This paper presents a methodology for probabilistic assessment of bearing capacity and prediction of failure mechanism of masonry vaults at the ultimate state with consideration of the natural variability of Young’s modulus of stones. First, the computation model is explained. The failure mode is the most reported mode, i.e. the four-hinge mechanism. Based on this assumption, the study of a vault composed of 16 segments is presented. The Young’s modulus of the segments is considered as random variable defined by a mean value and a coefficient of variation CV. A relationship linking the vault bearing capacity to the modulus variation of voussoirs is proposed. The failure mechanisms, in addition to that observed in the deterministic case, are identified for each CV value as well as their probability of occurrence. The results show that the mechanism observed in the deterministic case has decreasing probability of occurrence in terms of CV, while the number of other mechanisms and their probability of occurrence increase with the coefficient of variation of Young’s modulus. This means that if a significant change in the Young modulus of the segments is proven, taken it into account in computations becomes mandatory, both for determining the vault bearing capacity and for predicting its failure mechanism.

Keywords: masonry, mechanism, probability, variability, vault

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Authors: Wararit Panichkitkosolkul

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The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.

Keywords: autoregressive, ordinary least squares, type i error, power of the test, Monte Carlo simulation

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

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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

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Authors: Manoel Pereira, Alvaro Veiga, Camila Epprecht, Renato Costa

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This paper introduces an empirical version of the Esscher transform for risk-neutral option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying. In our proposal, we make only mild assumptions on the pricing kernel and there is no need for the formulation of the risk-neutral model for the returns. First, we simulate sample paths for the returns under the physical distribution. Then, based on the empirical Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a weighted sum of the options pay-offs in each path. We compare our proposal with some traditional parametric pricing methods in four experiments with artificial and real data.

Keywords: esscher transform, generalized autoregressive Conditional Heteroscedastic (GARCH), nonparametric option pricing

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Authors: Serge Provost, Yishan Zang

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Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.

Keywords: arctangent transformation, tail classification, heavy-tailed distributions, distributional moments

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Authors: Alhusein Almahjoub, Dongyu Qiu

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This paper deals with the random access procedure in next-generation networks and presents the solution to reduce total service time (TST) which is one of the most important performance metrics in current and future internet of things (IoT) based networks. The proposed solution focuses on the calculation of optimal transmission probability which maximizes the success probability and reduces TST. It uses the information of several idle preambles in every time slot, and based on it, it estimates the number of backlogged IoT devices using Naïve Bayes estimation which is a type of supervised learning in the machine learning domain. The estimation of backlogged devices is necessary since optimal transmission probability depends on it and the eNodeB does not have information about it. The simulations are carried out in MATLAB which verify that the proposed solution gives excellent performance.

Keywords: random access, LTE/LTE-A, 5G, machine learning, Naïve Bayes estimation

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Authors: Elzbieta Babula, Juhyun Park

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Tversky and Kahneman’s cumulative prospect theory assumes symmetric probability cumulation with regard to the reference point within decision weights. Theoretically, this model should be invariant under the change of the direction of probability cumulation. In the present study, this phenomenon is being investigated by creating a reference model that allows verifying the parameter interactions in the cumulative prospect theory specifications. The simultaneous parametric fitting of utility and weighting functions is applied to binary choice data from the experiment. The results show that the flexibility of the probability weighting function is a crucial characteristic allowing to prevent parameter interactions while estimating cumulative prospect theory.

Keywords: binary choice experiment, cumulative prospect theory, decision weights, parameter interactions

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Authors: D. De-León-Escobedo, D. J. Delgado-Hernández, S. Pérez

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A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.

Keywords: expected life-cycle cost, failure probability, slopes failure, storms

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Authors: Golnaz Shahtahmassebi, Jose Maria Sarabia

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In this talk, we introduce a new class of conjugate prior distributions obtained from conditional specification methodology. We illustrate the application of such distribution in Bayesian change point detection in Poisson processes. We obtain the posterior distribution of model parameters using a general bivariate distribution with gamma conditionals. Simulation from the posterior is readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Keywords: change point, bayesian inference, Gibbs sampler, conditional specification, gamma conditional distributions

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Authors: Meimei Wen, Chang Nyung Kim

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In the current study, three-dimensional liquid metal (LM) magneto-hydrodynamic (MHD) flows in a manifold with three sub-channels under a uniform magnetic field are numerically investigated. In the manifold, the electrical current can cross channel walls, thus having influence on the flow distribution in each sub-channel. A case with various arrangements of electric conductivity for different parts of channel walls is considered, yielding different current distributions as well as flow distributions in each sub-channel. Here, the imbalance of mass flow rates in the three sub-channels is addressed. Meanwhile, predicted are detailed behaviors of the flow velocity, pressure, current and electric potential of LM MHD flows with three sub-channels. Commercial software CFX is used for the numerical simulation of LM MHD flows.

Keywords: CFX, liquid metal, manifold, MHD flow

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