Search results for: quantile function model

Authors: Yuzhi Cai

Abstract:

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: Yoonsuh Jung, Steven N. MacEachern

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Check loss function is used to define quantile regression. In the prospect of cross validation, it is also employed as a validation function when underlying truth is unknown. However, our empirical study indicates that the validation with check loss often leads to choosing an over estimated fits. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. It has a large effect of guarding against over fitted model in some extent. Through various simulation settings of linear and non-linear regressions, the improvement of check loss by L2 adjustment is empirically examined. This adjustment is devised to shrink to zero as sample size grows.

Keywords: cross-validation, model selection, quantile regression, tuning parameter selection

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Authors: Niya Chen, Jennifer Chan

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In the financial market, risk management helps to minimize potential loss and maximize profit. There are two ways to assess risks; the first way is to calculate the risk directly based on the volatility. The most common risk measurements are Value at Risk (VaR), sharp ratio, and beta. Alternatively, we could look at the quantile of the return to assess the risk. Popular return models such as GARCH and stochastic volatility (SV) focus on modeling the mean of the return distribution via capturing the volatility dynamics; however, the quantile/expectile method will give us an idea of the distribution with the extreme return value. It will allow us to forecast VaR using return which is direct information. The advantage of using these non-parametric methods is that it is not bounded by the distribution assumptions from the parametric method. But the difference between them is that expectile uses a second-order loss function while quantile regression uses a first-order loss function. We consider several quantile functions, different volatility measures, and estimates from some volatility models. To estimate the expectile of the model, we use Realized Conditional Autoregressive Expectile (CARE) model with the bayesian method to achieve this. We would like to see if our proposed models outperform existing models in cryptocurrency, and we will test it by using Bitcoin mainly as well as Ethereum.

Keywords: expectile, CARE Model, CARR Model, quantile, cryptocurrency, Value at Risk

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Authors: Yuzhi Cai

Abstract:

In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: combining forecasts, MCMC, predictive density functions, quantile forecasting, quantile modelling

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Authors: Kajingulu Malandala, Ranganai Edmore

Abstract:

The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

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Authors: Ishapathik Das

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The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs

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Authors: S. H. Arnaud Kanga, O. Hili, S. Dabo-Niang

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Spatial prediction is an issue appealing and attracting several fields such as agriculture, environmental sciences, ecology, econometrics, and many others. Although multiple non-parametric prediction methods exist for spatial data, those are based on the conditional expectation. This paper took a different approach by examining a non-parametric spatial predictor of the conditional quantile. The study especially observes the stationary multidimensional spatial process over a rectangular domain. Indeed, the proposed quantile is obtained by inverting the conditional distribution function. Furthermore, the proposed estimator of the conditional distribution function depends on three kernels, where one of them controls the distance between spatial locations, while the other two control the distance between observations. In addition, the almost complete convergence and the convergence in mean order q of the kernel predictor are obtained when the sample considered is alpha-mixing. Such approach of the prediction method gives the advantage of accuracy as it overcomes sensitivity to extreme and outliers values.

Keywords: conditional quantile, kernel, nonparametric, stationary

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Authors: Yuzhi Cai

Abstract:

This talk presents a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated MCMC algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out-of-sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. An application of the method to the USD to GBP daily currency exchange rates will also be discussed. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.

Keywords: combining forecasts, MCMC, quantile modelling, quantile forecasting, predictive density functions

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

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Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: bootstrap, edgeworth approximation, IID, quantile

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Authors: Yaeji Lim, Hee-Seok Oh

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The coherence analysis measures the linear time-invariant relationship between two data sets and has been studied various fields such as signal processing, engineering, and medical science. However classical coherence analysis tends to be sensitive to outliers and focuses only on mean relationship. In this paper, we generalized cross periodogram to quantile cross periodogram and provide richer inter-relationship between two data sets. This is a general version of Laplace cross periodogram. We prove its asymptotic distribution under the long range process and compare them with ordinary coherence through numerical examples. We also present real data example to confirm the usefulness of quantile coherence analysis.

Keywords: coherence, cross periodogram, spectrum, quantile

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Authors: Gamze Ozel, Selen Cakmakyapan

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We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of real life data set.

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood

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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: Rene Valdiviezo-Issa

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In this paper, we use Mexico’s Households Income and Expenditures (ENIGH) survey to explain the behaviour that the urban-rural expenditure gap has had since Mexico’s incorporation to the North American Free Trade Agreement (NAFTA) in 1994 and we compare it with the latest available survey, which took place in 2014. We use real trimestral expenditure per capita (RTEPC) as the measure of welfare. We use quantile regressions and a quantile regression decomposition to describe the gap between urban and rural distributions of log RTEPC. We discover that the decrease in the difference between the urban and rural distributions of log RTEPC, or inequality, is motivated because of a deprivation of the urban areas, in very specific characteristics, rather than an improvement of the urban areas. When using the decomposition we observe that the gap is primarily brought about because differences in returns to covariates between the urban and rural areas.

Keywords: quantile regression, urban-rural inequality, inequality in Mexico, income decompositon

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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

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

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The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: area-based traffic, car-following model, micro-simulation, stochastic modeling

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Authors: Komlan Sedzro

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We apply the non-parametric, unconditional, hyperbolic order-α quantile estimator to appraise the relative efficiency of Microfinance Institutions in Africa in terms of outreach. Our purpose is to verify if these institutions, which must constantly try to strike a compromise between their social role and financial sustainability are operationally efficient. Using data on African MFIs extracted from the Microfinance Information eXchange (MIX) database and covering the 2004 to 2006 periods, we find that more efficient MFIs are also the most profitable. This result is in line with the view that social performance is not in contradiction with the pursuit of excellent financial performance. Our results also show that large MFIs in terms of asset and those charging the highest fees are not necessarily the most efficient.

Keywords: data envelopment analysis, microfinance institutions, quantile estimation of efficiency, social and financial performance

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Authors: Charles-Olivier Amédée-Manesme, Benoit Faye, Eric Le Fur

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In this paper, the heterogeneity of the Bordeaux Legends 50 wine market price segment is addressed. For this purpose, quantile regression is applied – with market segmentation based on wine bottle price quantile – and the hedonic price of wine attributes is computed for various price segments of the market. The approach is applied to a major privately held data set which consists of approximately 30,000 transactions over the 2003–2014 period. The findings suggest that the relative hedonic prices of several wine attributes differ significantly among deciles. In particular, the elasticity coefficient of the expert ratings shows strong variation among prices. If - as suggested in the literature - expert ratings have a positive influence on wine price on average, they have a clearly decreasing impact over the quantiles. Finally, the lower the wine price, the higher the potential for price appreciation over time. Other variables such as chateaux or vintage are also shown to vary across the distribution of wine prices. While enhancing our understanding of the complex market dynamics that underlie Bordeaux wines’ price, this research provides empirical evidence that the QR approach adequately captures heterogeneity among wine price ranges, which simultaneously applies to wine stock, vintage and auctions’ house.

Keywords: hedonics, market segmentation, quantile regression, heterogeneity, wine economics

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Authors: Priya Kedia, Kiranmoy Das

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There is a rich literature on variable selection in regression setting. However, most of these methods assume normality for the response variable under consideration for implementing the methodology and establishing the statistical properties of the estimates. In many real applications, the distribution for the response variable may be non-Gaussian, and one might be interested in finding the best subset of covariates at some predetermined quantile level. We develop dynamic Bayesian approach for variable selection in quantile regression framework. We use a zero-inflated mixture prior for the regression coefficients, and consider the asymmetric Laplace distribution for the response variable for modeling different quantiles of its distribution. An efficient Gibbs sampler is developed for our computation. Our proposed approach is assessed through extensive simulation studies, and real application of the proposed approach is also illustrated. We consider the data from health and retirement study conducted by the University of Michigan, and select the important predictors when the outcome of interest is out-of-pocket medical cost, which is considered as an important measure for financial risk. Our analysis finds important predictors at different quantiles of the outcome, and thus enhance our understanding on the effects of different predictors on the out-of-pocket medical cost.

Keywords: variable selection, quantile regression, Gibbs sampler, asymmetric Laplace distribution

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Authors: Nattabhorn Leamcharaskul

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This study aims to examine determining factors of the dynamics of poverty in Thailand by using panel data of 3,567 households in 2007-2017. Four techniques of estimation are employed to analyze the situation of poverty across households and time periods: the multinomial logit model, the sequential logit model, the quantile regression model, and the difference in difference model. Households are categorized based on their experiences into 5 groups, namely chronically poor, falling into poverty, re-entering into poverty, exiting from poverty and never poor households. Estimation results emphasize the effects of demographic and socioeconomic factors as well as unexpected events on the economic status of a household. It is found that remittances have positive impact on household’s economic status in that they are likely to lower the probability of falling into poverty or trapping in poverty while they tend to increase the probability of exiting from poverty. In addition, not only receiving a secondary source of household income can raise the probability of being a never poor household, but it also significantly increases household income per capita of the chronically poor and falling into poverty households. Public work programs are recommended as an important tool to relieve household financial burden and uncertainty and thus consequently increase a chance for households to escape from poverty.

Keywords: difference in difference, dynamic, multinomial logit model, panel data, poverty, quantile regression, remittance, sequential logit model, Thailand, transfer

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Authors: Chiung-Ju Huang

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This study utilizes the quantile regression analysis to examine the impact of governance (including democratic quality and technical quality) on happiness in 101 countries worldwide, classified as “developed countries” and “developing countries”. The empirical results show that the impact of democratic quality and technical quality on happiness is significantly positive for “developed countries”, while is insignificant for “developing countries”. The results suggest that the authorities in developed countries can enhance the level of individual happiness by means of improving the democracy quality and technical quality. However, for developing countries, promoting the quality of governance in order to enhance the level of happiness may not be effective. Policy makers in developed countries may pay more attention on increasing real GDP per capita instead of promoting the quality of governance to enhance individual happiness.

Keywords: governance, happiness, multiple regression, quantile regression

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Authors: Wenbo Du, Xiaomei Ma

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With the empowerment of Cognitive Diagnostic Assessment (CDA), various domains of language testing and assessment have been investigated to dig out more diagnostic information. What is noticeable is that most of the extant empirical CDA-based research puts much emphasis on individual-level diagnostic purpose with very few concerned about learners’ group-level performance. Even though the personalized diagnostic feedback is the unique feature that differentiates CDA from other assessment tools, group-level diagnostic information cannot be overlooked in that it might be more practical in classroom setting. Additionally, the group-level diagnostic information obtained via current CDA always results in a “flat pattern”, that is, the mastery/non-mastery of all tested skills accounts for the two highest proportion. In that case, the outcome does not bring too much benefits than the original total score. To address these issues, the present study attempts to apply cluster analysis for group classification and quantile regression analysis to pinpoint learners’ performance at different proficiency levels (beginner, intermediate and advanced) thus to enhance the interpretation of the CDA results extracted from a group of EFL learners’ reading performance on a diagnostic reading test designed by PELDiaG research team from a key university in China. The results show that EM method in cluster analysis yield more appropriate classification results than that of CDA, and quantile regression analysis does picture more insightful characteristics of learners with different reading proficiencies. The findings are helpful and practical for instructors to refine EFL reading curriculum and instructional plan tailored based on the group classification results and quantile regression analysis. Meanwhile, these innovative statistical methods could also make up the deficiencies of CDA and push forward the development of language testing and assessment in the future.

Keywords: cognitive diagnostic assessment, diagnostic feedback, EFL reading, quantile regression

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Authors: Ender Su, Kai Wen Wong, I-Ling Ju, Ya-Ling Wang

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In this study, the systemic risk change of Taiwan’s banking sector is analyzed during the financial crisis. The risk expose of each financial institutions to the whole Taiwan banking systemic risk or vice versa under financial distress are measured by conditional Value-at-Risk (CoVaR) and conditional coherent expected shortfall (CoES). The CoVaR and CoES are estimated by using vector quantile autoregression (MVMQ-CaViaR) with the daily stock returns of each banks included domestic and foreign banks in Taiwan. The daily in-sample data covered the period from 05/20/2002 to 07/31/2007 and the out-of-sample period until 12/31/2013 spanning the 2008 U.S. subprime crisis, 2010 Greek debt crisis, and post risk duration. All banks in Taiwan are categorised into several groups according to their size of market capital, leverage and domestic/foreign to find out what the extent of changes of the systemic risk as the risk changes between the individuals in the bank groups and vice versa. The final results can provide a guidance to financial supervisory commission of Taiwan to gauge the downside risk in the system of financial institutions and determine the minimum capital requirement hold by financial institutions due to the sensibility changes in CoVaR and CoES of each banks.

Keywords: bank financial distress, vector quantile autoregression, CoVaR, CoES

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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: Jann-Eike Saathoff, Kirill Alexander Schmoor, Martin Achmus, Mauricio Terceros

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By using partial factors of safety, uncertainties due to the inherent variability of the soil properties and loads are taken into account in the geotechnical design process. According to the reliability index concept in Eurocode-0 in conjunction with Eurocode-7 a minimum safety level of β = 3.8 for reliability class RC2 shall be established. The reliability of the system depends heavily on the choice of the prespecified safety factor and the choice of the characteristic soil properties. The safety factors stated in the standards are mainly based on experience. However, no general accepted method for the calculation of a characteristic value within the current design practice exists. In this study, a laterally loaded monopile is investigated and the influence of the chosen quantile values of the deterministic system, calculated with p-y springs, will be presented. Monopiles are the most common foundation concepts for offshore wind energy converters. Based on the calculations for non-cohesive soils, a recommendation for an appropriate quantile value for the necessary safety level according to the standards for a deterministic design is given.

Keywords: asymptotic sampling, characteristic value, monopile foundation, probabilistic design, quantile values

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Authors: Yuan Zheng

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3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.

Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information

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Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: Samuel Oluwafemi Oyamakin, Angela Unna Chukwu

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Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.

Keywords: height, diameter at breast height, DBH, hyperbolic sine function, Pinus caribaea, Richards' growth model

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Authors: Balazs Somodi, Balazs Kovesdi

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In the research praxis of civil engineering the statistical evaluation of experimental and numerical investigations is an essential task in order to compare the experimental and numerical resistances of a specific structural problem with the proposed resistances of the standards. However, in the standards and in the international literature there are several different safety factor evaluation methods that can be used to check the necessary safety level (e.g.: 5% quantile level, 2.3% quantile level, 1‰ quantile level, γM partial safety factor, γM* partial safety factor, β reliability index). Moreover, in the international literature different calculation methods could be found even for the same safety factor as well. In the present study the flexural buckling resistance of high strength steel (HSS) welded closed sections are analyzed. The authors investigated the flexural buckling resistances of the analyzed columns by laboratory experiments. In the present study the safety levels of the obtained experimental resistances are calculated based on several safety approaches and compared with the EN 1990. The results of the different safety approaches are compared and evaluated. Based on the evaluation tendencies are identified and the differences between the statistical evaluation methods are explained.

Keywords: flexural buckling, high strength steel, partial safety factor, statistical evaluation

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Authors: Shlomit Hon-Snir, Sharon Teitler-Regev, Anabel Lifszyc Friedlander

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Tourism, one of the world's largest and fastest growing industries, exerts a major economic influence. The number of international tourists is growing every year, and the relative portion of independent (FIT) tourists is growing as well. The characteristics of independent tourists differ from those of tourists who travel in organized trips. The purpose of the research is to identify the factors that affect the individual tourist's expenses in Israel: total expenses, expenses per day, expenses per tourist, expenses per day per tourist, accommodation expenses, dining expenses and transportation expenses. Most of the research analyzed the total expenses using OLS regression. The determinants influencing expenses were divided into four groups: budget constraints, socio-demographic data, psychological characteristics and travel-related characteristics. Since the effect of each variable may change over different levels of total expenses the quantile regression (QR) theory will be applied. The current research will use data collected by the Israeli Ministry of Tourism in 2015 from individual independent tourists at the end of their visit to Israel. Preliminary results show that: At lower levels of expense, only income has a (positive) effect on total expenses, while at higher levels of expense, both income and length of stay have (positive) effects. -The effect of income on total expenses is higher for higher levels of expenses than for lower level of expenses. -The number of sites visited during the trip has a (negative) effect on tourist accommodation expenses only for tourists with a high level of total expenses. Due to the increasing share of independent tourism in Israel and around the world and due to the importance of tourism to Israel, it is very important to understand the factors that influence the expenses and behavior of independent tourists. Understanding the factors that affect independent tourists' expenses in Israel can help Israeli policymakers in their promotional efforts to attract tourism to Israel.

Keywords: independent tourist, quantile regression theory, tourism expenses, tourism

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