Search results for: skewed distributions

Authors: Derya Karagöz

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A Shewhart chart based on normality assumption is not appropriate for skewed distributions since its Type-I error rate is inflated. This study presents X̄ and S control charts for monitoring the process variability for skewed distributions. We propose Weighted Standard Deviation (WSD) X̄ and S control charts. Standard deviation estimator is applied to monitor the process variability for estimating the process standard deviation, in the case of the W SD X̄ and S control charts as this estimator is simple and easy to compute. Unlike the Shewhart control chart, the proposed charts provide asymmetric limits in accordance with the direction and degree of skewness to construct the upper and lower limits. The performances of the proposed charts are compared with other heuristic charts for skewed distributions by using Simulation study. The Simulation studies show that the proposed control charts have good properties for skewed distributions and large sample sizes.

Keywords: weighted standard deviation, MAD, skewed distributions, S control charts

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Authors: Timothy Kayode Samson, Adedoyin Isola Lawal

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The past five years have shown a sharp increase in public interest in the crypto market, with its market capitalization growing from $100 billion in June 2017 to $2158.42 billion on April 5, 2022. Despite the outrageous nature of the volatility of cryptocurrencies, the use of skewed error innovation distributions in modelling the volatility behaviour of these digital currencies has not been given much research attention. Hence, this study models the volatility of 5 largest cryptocurrencies by market capitalization (Bitcoin, Ethereum, Tether, Binance coin, and USD Coin) using four variants of GARCH models (GJR-GARCH, sGARCH, EGARCH, and APARCH) estimated using three skewed error innovation distributions (skewed normal, skewed student- t and skewed generalized error innovation distributions). Daily closing prices of these currencies were obtained from Yahoo Finance website. Finding reveals that the Binance coin reported higher mean returns compared to other digital currencies, while the skewness indicates that the Binance coin, Tether, and USD coin increased more than they decreased in values within the period of study. For both Bitcoin and Ethereum, negative skewness was obtained, meaning that within the period of study, the returns of these currencies decreased more than they increased in value. Returns from these cryptocurrencies were found to be stationary but not normality distributed with evidence of the ARCH effect. The skewness parameters in all best forecasting models were all significant (p<.05), justifying of use of skewed error innovation distributions with a fatter tail than normal, Student-t, and generalized error innovation distributions. For Binance coin, EGARCH-sstd outperformed other volatility models, while for Bitcoin, Ethereum, Tether, and USD coin, the best forecasting models were EGARCH-sstd, APARCH-sstd, EGARCH-sged, and GJR-GARCH-sstd, respectively. This suggests the superiority of skewed Student t- distribution and skewed generalized error distribution over the skewed normal distribution.

Keywords: skewed generalized error distribution, skewed normal distribution, skewed student t- distribution, APARCH, EGARCH, sGARCH, GJR-GARCH

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Authors: Rana Rimawi, Ayman Baklizi

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Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

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Authors: Jayanta Pokharel, Gokarna Aryal, Netra Kanaal, Chris Tsokos

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Investment in stocks and shares aims to seek potential gains while weighing the risk of future needs, such as retirement, children's education etc. Analysis of the behavior of the stock market returns and making prediction is important for investors to mitigate risk on investment. Historically, the normal variance models have been used to describe the behavior of stock market returns. However, the returns of the financial assets are actually skewed with higher kurtosis, heavier tails, and a higher center than the normal distribution. The Laplace distribution and its family are natural candidates for modeling stock returns. The Variance-Gamma (VG) distribution is the most sought-after distributions for modeling asset returns and has been extensively discussed in financial literatures. In this paper, it explore the other Laplace family, such as Asymmetric Laplace, Skewed Laplace, Kumaraswamy Laplace (KS) together with Variance-Gamma to model the weekly returns of the S&P 500 Index and it's eleven business sector indices. The method of maximum likelihood is employed to estimate the parameters of the distributions and our empirical inquiry shows that the Kumaraswamy Laplace distribution performs much better for stock returns modeling among the choice of distributions used in this study and in practice, KS can be used as a strong alternative to VG distribution.

Keywords: stock returns, variance-gamma, kumaraswamy laplace, maximum likelihood

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Authors: İlhami Karahanoglu, Oguz Ceylan

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As its well-known definitions; systemic risk refers to whole economic system down-turn movement even collapse together in very severe cases. In fact, it points out the contagion effects of the defaults. Such a risk is can be depicted with the famous Chinese game of falling domino stones. During and after the Bear & Sterns and Lehman Brothers cases, it was well understood that there is a very strong effect of systemic risk in financial services sector. In this study, we concentrate on the existence of systemic risk in Turkish Banking Sector based upon the Halkbank Case during the end month of 2013; there was a political turmoil in Turkey in which the close relatives of the upper politicians were involved in illegal trading activities. In that operation, the CEO of Halkbank was also arrested and in investigation, Halkbank was considered as part of such illegal actions. That operation had an impact on Halkbanks stock value. The Halkbank stock value during that time interval decreased remarkably, the distributional profile of stock return changed and became more volatile as well as more skewed. In this study, the daily returns of 5 leading banks in Turkish banking sector were used to obtain 48 return distributions (for each month, 90-days-back stock value returns are used) of 5 banks for the period 12/2011-12/2013 (pre operation period) and 12/2013-12/2015 (post operation period). When those distributions are compared with timely manner, interestingly; the distribution of the 5 other leading banks in Turkey, public or private, had also distribution profiles which was different from the past 2011-2013 period just like Halkbank. Those 5 big banks, whose stock values are monitored with sub index in Istanbul stock exchange (BIST) as BN10, had more skewed distribution just following the Halkbank stock return movement during the post operation period, with lover mean value and as well higher volatility. In addition, the correlation between the stock value return distributions of the leading banks after Halkbank case, where the returns are more skewed to the left, increased (which is measured in monthly base before and after the operation). The dependence between those banks was stronger under the case where the stock values were falling compared with the normal market condition. Such distributional effect of stock returns between the leading banks in Turkey, which is valid for down sub-market (financial/banking sector) condition, can be evaluated as an evidence for the existence of contagious effect and systemic risk.

Keywords: financial risk, systemic risk, banking sector, return distribution, dependency structure

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Authors: Mohadeseh Shojaei Shahrokhabadi, Ding-Geng (Din) Chen

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Positive continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical cost data. To jointly model semi-continuous longitudinal cost data and survival data and to provide marginalized covariate effect estimates, a marginalized two-part joint model (MTJM) has been developed for outcome variables with lognormal distributions. In this paper, we propose MTJM models for outcome variables from a generalized gamma (GG) family of distributions. The GG distribution constitutes a general family that includes approximately all of the most frequently used distributions like the Gamma, Exponential, Weibull, and Log Normal. In the proposed MTJM-GG model, the conditional mean from a conventional two-part model with a three-parameter GG distribution is parameterized to provide the marginal interpretation for regression coefficients. In addition, MTJM-gamma and MTJM-Weibull are developed as special cases of MTJM-GG. To illustrate the applicability of the MTJM-GG, we applied the model to a set of real electronic health record data recently collected in Iran, and we provided SAS code for application. The simulation results showed that when the outcome distribution is unknown or misspecified, which is usually the case in real data sets, the MTJM-GG consistently outperforms other models. The GG family of distribution facilitates estimating a model with improved fit over the MTJM-gamma, standard Weibull, or Log-Normal distributions.

Keywords: marginalized two-part model, zero-inflated, right-skewed, semi-continuous, generalized gamma

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Authors: Rafida M. Elobaid

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Most of the literature on goodness-of-fit test try to provide a theoretical basis for studying empirical distribution functions. Such goodness-of-fit tests are Kolmogorove-Simirnov and Crumer-Von Mises Type tests. However, it is likely that most of literature has not focused in details on the relationship of the values of the test statistics and skewness or kurtosis. The aim of this study is to investigate the behavior of the values of the χ2 test statistic with the variation of the skewness of right skewed distribution. A simulation study is conducted to generate random numbers from Weibull distribution. For a fixed sample sizes, different levels of skewness are considered, and the corresponding values of the χ2 test statistic are calculated. Using different sample sizes, the results show an inverse relationship between the value of χ2 test and the level of skewness for Wiebull distribution, i.e the value of χ2 test statistic decreases as the value of skewness increases. The research results also show that with large values of skewness we are more confident that the data follows the assumed distribution. Nonparametric Kendall τ test is used to confirm these results.

Keywords: goodness-of-fit test, chi-square test, simulation, continuous right skewed distributions

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Authors: D. K. Rao, M. G. M. Khan, K. G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries (OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy is skewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB is formulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: stratified sampling, optimum strata boundaries, optimum sample size, pareto distribution, mathematical programming problem, dynamic programming technique

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Authors: Yih-Wenn Laih

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In recent times, the dependence and co-movement among international financial markets have become stronger than in the past, as evidenced by commentaries in the news media and the financial sections of newspapers. Studying the co-movement between returns in financial markets is an important issue for portfolio management and risk management. The realization of co-movement helps investors to identify the opportunities for international portfolio management in terms of asset allocation and pricing. Since the election of the new Prime Minister, Shinzo Abe, in November 2012, the yen has weakened against the US dollar from the 80 to the 120 level. The policies, known as “Abenomics,” are to encourage private investment through a more aggressive mix of monetary and fiscal policy. Given the close economic relations and competitions among Asia markets, it is interesting to discover the co-movement relations, affected by the depreciation of yen, between stock market of Japan and 5 major Asia stock markets, including China, Hong Kong, Korea, Singapore, and Taiwan. Specifically, we devote ourselves to measure the co-movement of stock markets between Japan and each one of the 5 Asia stock markets in terms of rank correlation coefficients. To compute the coefficients, return series of each stock market is first fitted by a skewed-t GARCH (generalized autoregressive conditional heteroscedasticity) model. Secondly, to measure the dependence structure between matched stock markets, we employ the symmetrized Joe-Clayton (SJC) copula to calculate the probability density function of paired skewed-t distributions. The joint probability density function is then utilized as the scoring scheme to optimize the sequence alignment by dynamic programming method. Finally, we compute the rank correlation coefficients (Kendall's  and Spearman's ) between matched stock markets based on their aligned sequences. We collect empirical data of 6 stock indexes from Taiwan Economic Journal. The data is sampled at a daily frequency covering the period from January 1, 2013 to July 31, 2015. The empirical distributions of returns indicate fatter tails than the normal distribution. Therefore, the skewed-t distribution and SJC copula are appropriate for characterizing the data. According to the computed Kendall’s τ, Korea has the strongest co-movement relation with Japan, followed by Taiwan, China, and Singapore; the weakest is Hong Kong. On the other hand, the Spearman’s ρ reveals that the strength of co-movement between markets with Japan in decreasing order are Korea, China, Taiwan, Singapore, and Hong Kong. We explore the effects of “Abenomics” on Asia stock markets by measuring the co-movement relation between Japan and five major Asia stock markets in terms of rank correlation coefficients. The matched markets are aligned by a hybrid method consisting of GARCH, copula and sequence alignment. Empirical experiments indicate that Korea has the strongest co-movement relation with Japan. The strength of China and Taiwan are better than Singapore. The Hong Kong market has the weakest co-movement relation with Japan.

Keywords: co-movement, depreciation of Yen, rank correlation, stock market

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Authors: Serpil Türkyılmaz, Mesut Balıbey

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In this study, long memory properties in volatility of Turkey Stock Market are being examined through the FIGARCH, FIEGARCH and FIAPARCH models under different distribution assumptions as normal and skewed student-t distributions. Furthermore, structural changes in volatility of Turkey Stock Market are investigated. The results display long memory property and the presence of asymmetric effects of shocks in volatility of Turkey Stock Market.

Keywords: FIAPARCH model, FIEGARCH model, FIGARCH model, structural break

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Authors: Hazem M. Al-Mofleh

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In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized Hyperbolic Secant Distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Rényi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

Keywords: bimodality, estimation, hazard function, moments, Shannon’s entropy

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Authors: M. T. Alodat

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In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions.

Keywords: normal distribution, moments, Fisher information, symmetric distributions

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Authors: Giriraj Achari, Malay Bhattacharyya

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In this paper, the effectiveness of Copula Markov Switching Multifractal (MSM) models at forecasting Value-at-Risk of a two-stock portfolio is studied. The innovations are allowed to be drawn from distributions that can capture skewness and leptokurtosis, which are well documented empirical characteristics observed in financial returns. The candidate distributions considered for this purpose are Johnson-SU, Pearson Type-IV and α-Stable distributions. The two univariate marginal distributions are combined using the Student-t copula. The estimation of all parameters is performed by Maximum Likelihood Estimation. Finally, the models are compared in terms of accurate Value-at-Risk (VaR) forecasts using tests of unconditional coverage and independence. It is found that Copula-MSM-models with leptokurtic innovation distributions perform slightly better than Copula-MSM model with Normal innovations. Copula-MSM models, in general, produce better VaR forecasts as compared to traditional methods like Historical Simulation method, Variance-Covariance approach and Copula-Generalized Autoregressive Conditional Heteroscedasticity (Copula-GARCH) models.

Keywords: Copula, Markov Switching, multifractal, value-at-risk

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Authors: Semra Turkan

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In this paper, we have examined the factors that affect the productivity of Turkey’s Top 500 Industrial Enterprises in 2014. The labor productivity of enterprises is taken as an indicator of productivity of industrial enterprises. When the relationships between some financial ratios and labor productivity, it is seen that there is a nonparametric relationship between labor productivity and return on sales. In addition, the distribution of labor productivity of enterprises is right-skewed. If the dependent distribution is skewed, the quantile regression is more suitable for this data. Hence, the nonparametric relationship between labor productivity and return on sales by quantile smoothing splines.

Keywords: quantile regression, smoothing spline, labor productivity, financial ratios

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Authors: Zubdahe Noor, Haseeb Athar

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In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

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Authors: Mohamed Barbary, Mohamed H. Abd El-Azeem

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Maneuvering extended object tracking (M-EOT) using high-resolution inverse synthetic aperture radar (ISAR) observations has been gaining momentum recently. This work presents a new robust implementation of the multiple models (MM) multi-Bernoulli (MB) filter for M-EOT, where the M-EOT’s ISAR observations are characterized using a skewed (SK) non-symmetrically normal distribution. To cope with the possible abrupt change of kinematic state, extension, and observation distribution over an extended object when a target maneuvers, a multiple model technique is represented based on MB-track-before-detect (TBD) filter supported by SK-sub-random matrix model (RMM) or sub-ellipses framework. Simulation results demonstrate this remarkable impact.

Keywords: maneuvering extended objects, ISAR, skewed normal distribution, sub-RMM, MM-MB-TBD filter

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Authors: David C. Ni

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Contemporary models for N-body systems are based on temporal, two-body, and mass point representation of Newtonian mechanics. Other mainstream models include 2D and 3D Ising models based on local neighborhood the lattice structures. In Quantum mechanics, the theories of collective modes are for superconductivity and for the long-range quantum entanglement. However, these models are still mainly for the specific phenomena with a set of designated parameters. We are therefore motivated to develop a new construction directly from the complex-variable N-body systems based on the extended Blaschke functions (EBF), which represent a non-temporal and nonlinear extension of Lorentz transformation on the complex plane – the normalized momentum spaces. A point on the complex plane represents a normalized state of particle momentums observed from a reference frame in the theory of special relativity. There are only two key parameters, normalized momentum and nonlinearity for modelling. An algorithm similar to Jenkins-Traub method is adopted for solving EBF iteratively. Through iteration, the solution sets show a form of σ + i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various distributions, such as 1-peak, 2-peak, and 3-peak etc. distributions and some of them are analog to the canonical distributions. The results of the numerical analysis demonstrate continuum-to-discreteness transitions, evolutional invariance of distributions, phase transitions with conjugate symmetry, etc., which manifest the construction as a potential candidate for the unification of statistics. We hereby classify the observed distributions on the finite convergent domains. Continuous and discrete distributions both exist and are predictable for given partitions in different regions of parameter-pair. We further compare these distributions with canonical distributions and address the impacts on the existing applications.

Keywords: blaschke, lorentz transformation, complex variables, continuous, discrete, canonical, classification

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Authors: Mohamed Barbary, Mohamed H. Abd El-azeem

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Maneuvering non-ellipsoidal extended object tracking (M-NEOT) using high-resolution inverse synthetic aperture radar (ISAR) observations is gaining momentum recently. This work presents a new robust implementation of the Jump Markov (JM) multi-Bernoulli (MB) filter for M-NEOT, where the M-NEOT’s ISAR observations are characterized using a skewed (SK) non-symmetrically normal distribution. To cope with the possible abrupt change of kinematic state, extension, and observation distribution over an extended object when a target maneuvers, a multiple model technique is represented based on an MB-track-before-detect (TBD) filter supported by SK-sub-random matrix model (RMM) or sub-ellipses framework. Simulation results demonstrate this remarkable impact.

Keywords: maneuvering extended objects, ISAR, skewed normal distribution, sub-RMM, JM-MB-TBD filter

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Authors: Yuzhi Cai

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In this paper, we introduce a newly developed quantile function model that can be used for estimating conditional distributions of financial returns and for obtaining multi-step ahead out-of-sample predictive distributions of financial returns. Since we forecast the whole conditional distributions, any predictive quantity of interest about the future financial returns can be obtained simply as a by-product of the method. We also show an application of the model to the daily closing prices of Dow Jones Industrial Average (DJIA) series over the period from 2 January 2004 - 8 October 2010. We obtained the predictive distributions up to 15 days ahead for the DJIA returns, which were further compared with the actually observed returns and those predicted from an AR-GARCH model. The results show that the new model can capture the main features of financial returns and provide a better fitted model together with improved mean forecasts compared with conventional methods. We hope this talk will help audience to see that this new model has the potential to be very useful in practice.

Keywords: DJIA, financial returns, predictive distribution, quantile function model

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Authors: Debasis Sengupta, Sudipta Das

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The class of life distributions with decreasing mean residual life (DMRL) is well known in the field of reliability modeling. It contains the IFR class of distributions and is contained in the NBUE class of distributions. While upper and lower bounds of the reliability distribution function of aging classes such as IFR, IFRA, NBU, NBUE, and HNBUE have discussed in the literature for a long time, there is no analogous result available for the DMRL class. We obtain the upper and lower bounds for the reliability function of the DMRL class in terms of first order finite moment. The lower bound is obtained by showing that for any fixed time, the minimization of the reliability function over the class of all DMRL distributions with a fixed mean is equivalent to its minimization over a smaller class of distribution with a special form. Optimization over this restricted set can be made algebraically. Likewise, the maximization of the reliability function over the class of all DMRL distributions with a fixed mean turns out to be a parametric optimization problem over the class of DMRL distributions of a special form. The constructive proofs also establish that both the upper and lower bounds are sharp. Further, the DMRL upper bound coincides with the HNBUE upper bound and the lower bound coincides with the IFR lower bound. We also prove that a pair of sharp upper and lower bounds for the reliability function when the distribution is increasing mean residual life (IMRL) with a fixed mean. This result is proved in a similar way. These inequalities fill a long-standing void in the literature of the life distribution modeling.

Keywords: DMRL, IMRL, reliability bounds, hazard functions

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Authors: Naci Büyükkaracığan

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Today, the need for water sources is swiftly increasing due to population growth. At the same time, it is known that some regions will face with shortage of water and drought because of the global warming and climate change. In this context, evaluation and analysis of hydrological data such as the observed trends, drought and flood prediction of short term flow has great deal of importance. The most accurate selection probability distribution is important to describe the low flow statistics for the studies related to drought analysis. As in many basins In Turkey, Gediz River basin will be affected enough by the drought and will decrease the amount of used water. The aim of this study is to derive appropriate probability distributions for frequency analysis of annual minimum flows at 6 gauging stations of the Gediz Basin. After applying 10 different probability distributions, six different parameter estimation methods and 3 fitness test, the Pearson 3 distribution and general extreme values distributions were found to give optimal results.

Keywords: Gediz Basin, goodness-of-fit tests, minimum flows, probability distribution

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Authors: Tasir Khan, Yejuan Wang

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The study of extreme rainfall events is very important for flood management in river basins and the design of water conservancy infrastructure. Evaluation of quantiles of annual maximum rainfall (AMRF) is required in different environmental fields, agriculture operations, renewable energy sources, climatology, and the design of different structures. Therefore, the annual maximum rainfall (AMRF) was performed at different stations in Pakistan. Multiple probability distributions, log normal (LN), generalized extreme value (GEV), Gumbel (max), and Pearson type3 (P3) were used to find out the most appropriate distributions in different stations. The L moments method was used to evaluate the distribution parameters. Anderson darling test, Kolmogorov- Smirnov test, and chi-square test showed that two distributions, namely GUM (max) and LN, were the best appropriate distributions. The quantile estimate of a multi-parameter PD offers extreme rainfall through a specific location and is therefore important for decision-makers and planners who design and construct different structures. This result provides an indication of these multi-parameter distribution consequences for the study of sites and peak flow prediction and the design of hydrological maps. Therefore, this discovery can support hydraulic structure and flood management.

Keywords: RAMSE, multiple frequency analysis, annual maximum rainfall, L-moments

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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Authors: Hannah F. Opayinka, Adedayo A. Adepoju

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This study is an extension of a prior study on the modification of the existing m-out-of-n (moon) bootstrap method for heavy-tailed distributions in which modified m-out-of-n (mmoon) was proposed as an alternative method to the existing moon technique. In this study, both moon and mmoon techniques were applied to two real income datasets which followed Lognormal and Pareto distributions respectively with finite variances. The performances of these two techniques were compared using Standard Error (SE) and Root Mean Square Error (RMSE). The findings showed that mmoon outperformed moon bootstrap in terms of smaller SEs and RMSEs for all the sample sizes considered in the two datasets.

Keywords: Bootstrap, income data, lognormal distribution, Pareto distribution

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Authors: Wilmer Osvaldo Martinez, Manuel Dario Hernandez, Juan Manuel Julio

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We propose to assess the performance of k forecast procedures by exploring the distributions of forecast errors and error losses. We argue that non systematic forecast errors minimize when their distributions are symmetric and unimodal, and that forecast accuracy should be assessed through stochastic loss order rather than expected loss order, which is the way it is customarily performed in previous work. Moreover, since forecast performance evaluation can be understood as a one way analysis of variance, we propose to explore loss distributions under two circumstances; when a strict (but unknown) joint stochastic order exists among the losses of all forecast alternatives, and when such order happens among subsets of alternative procedures. In spite of the fact that loss stochastic order is stronger than loss moment order, our proposals are at least as powerful as competing tests, and are robust to the correlation, autocorrelation and heteroskedasticity settings they consider. In addition, since our proposals do not require samples of the same size, their scope is also wider, and provided that they test the whole loss distribution instead of just loss moments, they can also be used to study forecast distributions as well. We illustrate the usefulness of our proposals by evaluating a set of real world forecasts.

Keywords: forecast evaluation, stochastic order, multiple comparison, non parametric test

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Authors: Thuvanan Borvornvitchotikarn, Werasak Kurutach

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Mutual information (MI) is widely used in medical image registration. In the different medical images analysis, it is difficult to choose an optimal bins size number for calculating the probability distributions in MI. As the result, this paper presents a new adaptive bins number selection approach that named a hybrid EMPCA-Scott approach. This work combines an expectation maximization principal component analysis (EMPCA) and the modified Scott’s rule. The proposed approach solves the binning problem from the various intensity values in medical images. Experimental results of this work show the lower registration errors compared to other adaptive binning approaches.

Keywords: mutual information, EMPCA, Scott, probability distributions

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Authors: Abderrazek Ben Maatoug, Ibrahim Fatnassi, Wassim Ben Ayed

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In this paper we investigate the issue of market risk quantification for Middle East and North Africa (MENA) Islamic market equity. We use Value-at-Risk (VaR) as a measure of potential risk in Islamic stock market, for long and short position, based on Riskmetrics model and the conditional parametric ARCH class model volatility with normal, student and skewed student distribution. The sample consist of daily data for the 2006-2014 of 11 Islamic stock markets indices. We conduct Kupiec and Engle and Manganelli tests to evaluate the performance for each model. The main finding of our empirical results show that (i) the superior performance of VaR models based on the Student and skewed Student distribution, for the significance level of α=1% , for all Islamic stock market indices, and for both long and short trading positions (ii) Risk Metrics model, and VaR model based on conditional volatility with normal distribution provides the best accurate VaR estimations for both long and short trading positions for a significance level of α=5%.

Keywords: value-at-risk, risk management, islamic finance, GARCH models

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Authors: Obioma Uche

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Due to the recent volatility in oil & gas prices as well as increased development of non-conventional resources, it has become even more essential to critically evaluate the profitability of petroleum prospects prior to making any investment decisions. Traditionally, simple Monte Carlo (MC) algorithms have been used to randomly sample probability distributions of economic and geological factors (e.g. price, OPEX, CAPEX, reserves, productive life, etc.) in order to obtain probability distributions for profitability metrics such as Net Present Value (NPV). In recent years, second-order MC algorithms have been shown to offer an advantage over simple MC techniques due to the added consideration of uncertainties associated with the probability distributions of the relevant variables. Here, a strategy for the application of the second-order MC technique to a case study is demonstrated to analyze its effectiveness as a tool for portfolio management.

Keywords: Monte Carlo algorithms, portfolio management, profitability, risk analysis

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Authors: Muna Mitchell, Akshay Parchure, Krishna Singaraju

Abstract:

There is an increasing need for medium- to long-span steel bridges with complex geometry due to site restrictions in developed areas. One of the solutions to grade separations in congested areas is to use longer spans on skewed supports that avoid at-grade obstructions limiting impacts to the foundation. Where vertical clearances are also a constraint, continuous steel girders can be used to reduce superstructure depths. Combining continuous long steel spans on severe skews can resolve the constraints at a cost. The behavior of skewed girders is challenging to analyze and design with subsequent complexity during fabrication and construction. As a part of a corridor improvement project, Walter P Moore designed two 1700-foot side-by-side bridges carrying four lanes of traffic in each direction over a railroad track. The bridges consist of prestressed concrete girder approach spans and three-span continuous steel plate girder units. The roadway design added complex geometry to the bridge with horizontal and vertical curves combined with superelevation transitions within the plate girder units. The substructure at the steel units was skewed approximately 56 degrees to satisfy the existing railroad right-of-way requirements. A horizontal point of curvature (PC) near the end of the steel units required the use flared girders and chorded slab edges. Due to the flared girder geometry, the cross-frame spacing in each bay is unique. Staggered cross frames were provided based on AASHTO LRFD and NCHRP guidelines for high skew steel bridges. Skewed steel bridges develop significant forces in the cross frames and rotation in the girder websdue to differential displacements along the girders under dead and live loads. In addition, under thermal loads, skewed steel bridges expand and contract not along the alignment parallel to the girders but along the diagonal connecting the acute corners, resulting in horizontal displacement both along and perpendicular to the girders. AASHTO LRFD recommends a 95 degree Fahrenheit temperature differential for the design of joints and bearings. The live load and the thermal loads resulted in significant horizontal forces and rotations in the bearings that necessitated the use of HLMR bearings. A unique bearing layout was selected to minimize the effect of thermal forces. The span length, width, skew, and roadway geometry at the bridges also required modular bridge joint systems (MBJS) with inverted-T bent caps to accommodate movement in the steel units. 2D and 3D finite element analysis models were developed to accurately determine the forces and rotations in the girders, cross frames, and bearings and to estimate thermal displacements at the joints. This paper covers the decision-making process for developing the framing plan, bearing configurations, joint type, and analysis models involved in the design of the high-skew three-span continuous steel plate girder bridges.

Keywords: complex geometry, continuous steel plate girders, finite element structural analysis, high skew, HLMR bearings, modular joint

Procedia PDF Downloads 146

Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization

Procedia PDF Downloads 87