Commenced in January 2007
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Edition: International
Paper Count: 4551

Search results for: generalized pareto distribution‎

4551 The Generalized Pareto Distribution as a Model for Sequential Order Statistics

Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian


‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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4550 Modeling of Maximum Rainfall Using Poisson-Generalized Pareto Distribution in Kigali, Rwanda

Authors: Emmanuel Iyamuremye


Extreme rainfall events have caused significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life. They also have significant social, economic, and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur, hence mitigating the consequences. Extreme value theory has been used widely in modeling extreme rainfall and in various disciplines, such as financial markets, the insurance industry, failure cases. Climatic extremes have been analyzed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions, which provides evidence of the importance of modeling extreme rainfall from different regions of the world. In this paper, we focused on Peak Over Thresholds approach, where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research also considers the use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Kigali. The results indicate that the proposed Poisson-GP distribution provides a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. The research also found a slow increase in return levels for maximum monthly rainfall for higher return periods, and further, the intervals are increasingly wider as the return period is increasing.

Keywords: exceedances, extreme value theory, generalized Pareto distribution, Poisson generalized Pareto distribution

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4549 A Flexible Pareto Distribution Using α-Power Transformation

Authors: Shumaila Ehtisham


In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

Procedia PDF Downloads 108
4548 An Extension of the Generalized Extreme Value Distribution

Authors: Serge Provost, Abdous Saboor


A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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4547 Point Estimation for the Type II Generalized Logistic Distribution Based on Progressively Censored Data

Authors: Rana Rimawi, Ayman Baklizi


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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4546 Extreme Value Modelling of Ghana Stock Exchange Indices

Authors: Kwabena Asare, Ezekiel N. N. Nortey, Felix O. Mettle


Modelling of extreme events has always been of interest in fields such as hydrology and meteorology. However, after the recent global financial crises, appropriate models for modelling of such rare events leading to these crises have become quite essential in the finance and risk management fields. This paper models the extreme values of the Ghana Stock Exchange All-Shares indices (2000-2010) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A conditional approach of the EVT was preferred and hence an ARMA-GARCH model was fitted to the data to correct for the effects of autocorrelation and conditional heteroscedastic terms present in the returns series, before EVT method was applied. The Peak Over Threshold (POT) approach of the EVT, which fits a Generalized Pareto Distribution (GPD) model to excesses above a certain selected threshold, was employed. Maximum likelihood estimates of the model parameters were obtained and the model’s goodness of fit was assessed graphically using Q-Q, P-P and density plots. The findings indicate that the GPD provides an adequate fit to the data of excesses. The size of the extreme daily Ghanaian stock market movements were then computed using the Value at Risk (VaR) and Expected Shortfall (ES) risk measures at some high quantiles, based on the fitted GPD model.

Keywords: extreme value theory, expected shortfall, generalized pareto distribution, peak over threshold, value at risk

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4545 Optimum Stratification of a Skewed Population

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


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

Procedia PDF Downloads 296
4544 Analysis of the Statistical Characterization of Significant Wave Data Exceedances for Designing Offshore Structures

Authors: Rui Teixeira, Alan O’Connor, Maria Nogal


The statistical theory of extreme events is progressively a topic of growing interest in all the fields of science and engineering. The changes currently experienced by the world, economic and environmental, emphasized the importance of dealing with extreme occurrences with improved accuracy. When it comes to the design of offshore structures, particularly offshore wind turbines, the importance of efficiently characterizing extreme events is of major relevance. Extreme events are commonly characterized by extreme values theory. As an alternative, the accurate modeling of the tails of statistical distributions and the characterization of the low occurrence events can be achieved with the application of the Peak-Over-Threshold (POT) methodology. The POT methodology allows for a more refined fit of the statistical distribution by truncating the data with a minimum value of a predefined threshold u. For mathematically approximating the tail of the empirical statistical distribution the Generalised Pareto is widely used. Although, in the case of the exceedances of significant wave data (H_s) the 2 parameters Weibull and the Exponential distribution, which is a specific case of the Generalised Pareto distribution, are frequently used as an alternative. The Generalized Pareto, despite the existence of practical cases where it is applied, is not completely recognized as the adequate solution to model exceedances over a certain threshold u. References that set the Generalised Pareto distribution as a secondary solution in the case of significant wave data can be identified in the literature. In this framework, the current study intends to tackle the discussion of the application of statistical models to characterize exceedances of wave data. Comparison of the application of the Generalised Pareto, the 2 parameters Weibull and the Exponential distribution are presented for different values of the threshold u. Real wave data obtained in four buoys along the Irish coast was used in the comparative analysis. Results show that the application of the statistical distributions to characterize significant wave data needs to be addressed carefully and in each particular case one of the statistical models mentioned fits better the data than the others. Depending on the value of the threshold u different results are obtained. Other variables of the fit, as the number of points and the estimation of the model parameters, are analyzed and the respective conclusions were drawn. Some guidelines on the application of the POT method are presented. Modeling the tail of the distributions shows to be, for the present case, a highly non-linear task and, due to its growing importance, should be addressed carefully for an efficient estimation of very low occurrence events.

Keywords: extreme events, offshore structures, peak-over-threshold, significant wave data

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4543 Parameter Estimation for the Mixture of Generalized Gamma Model

Authors: Wikanda Phaphan


Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

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4542 Statistical Analysis of Cables in Long-Span Cable-Stayed Bridges

Authors: Ceshi Sun, Yueyu Zhao, Yaobing Zhao, Zhiqiang Wang, Jian Peng, Pengxin Guo


With the rapid development of transportation, there are more than 100 cable-stayed bridges with main span larger than 300 m in China. In order to ascertain the statistical relationships among the design parameters of stay cables and their distribution characteristics, 1500 cables were selected from 25 practical long-span cable-stayed bridges. A new relationship between the first order frequency and the length of cable was found by conducting the curve fitting. Then, based on this relationship other interesting relationships were deduced. Several probability density functions (PDFs) were used to investigate the distributions of the parameters of first order frequency, stress level and the Irvine parameter. It was found that these parameters obey the Lognormal distribution, the Weibull distribution and the generalized Pareto distribution, respectively. Scatter diagrams of the three parameters were plotted and their 95% confidence intervals were also investigated.

Keywords: cable, cable-stayed bridge, long-span, statistical analysis

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4541 Population Size Estimation Based on the GPD

Authors: O. Anan, D. Böhning, A. Maruotti


The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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4540 The Normal-Generalized Hyperbolic Secant Distribution: Properties and Applications

Authors: Hazem M. Al-Mofleh


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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4539 Classical and Bayesian Inference of the Generalized Log-Logistic Distribution with Applications to Survival Data

Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa


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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4538 A Bivariate Inverse Generalized Exponential Distribution and Its Applications in Dependent Competing Risks Model

Authors: Fatemah A. Alqallaf, Debasis Kundu


The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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4537 Pressure Distribution, Load Capacity, and Thermal Effect with Generalized Maxwell Model in Journal Bearing Lubrication

Authors: M. Guemmadi, A. Ouibrahim


This numerical investigation aims to evaluate how a viscoelastic lubricant described by a generalized Maxwell model, affects the pressure distribution, the load capacity and thermal effect in a journal bearing lubrication. We use for the purpose the CFD package software completed by adapted user define functions (UDFs) to solve the coupled equations of momentum, of energy and of the viscoelastic model (generalized Maxwell model). Two parameters, viscosity and relaxation time are involved to show how viscoelasticity substantially affect the pressure distribution, the load capacity and the thermal transfer by comparison to Newtonian lubricant. These results were also compared with the available published results.

Keywords: journal bearing, lubrication, Maxwell model, viscoelastic fluids, computational modelling, load capacity

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4536 Multi-Objective Random Drift Particle Swarm Optimization Algorithm Based on RDPSO and Crowding Distance Sorting

Authors: Yiqiong Yuan, Jun Sun, Dongmei Zhou, Jianan Sun


In this paper, we presented a Multi-Objective Random Drift Particle Swarm Optimization algorithm (MORDPSO-CD) based on RDPSO and crowding distance sorting to improve the convergence and distribution with less computation cost. MORDPSO-CD makes the most of RDPSO to approach the true Pareto optimal solutions fast. We adopt the crowding distance sorting technique to update and maintain the archived optimal solutions. Introducing the crowding distance technique into MORDPSO can make the leader particles find the true Pareto solution ultimately. The simulation results reveal that the proposed algorithm has better convergence and distribution

Keywords: multi-objective optimization, random drift particle swarm optimization, crowding distance sorting, pareto optimal solution

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4535 The Application of Pareto Local Search to the Single-Objective Quadratic Assignment Problem

Authors: Abdullah Alsheddy


This paper presents the employment of Pareto optimality as a strategy to help (single-objective) local search escaping local optima. Instead of local search, Pareto local search is applied to solve the quadratic assignment problem which is multi-objectivized by adding a helper objective. The additional objective is defined as a function of the primary one with augmented penalties that are dynamically updated.

Keywords: Pareto optimization, multi-objectivization, quadratic assignment problem, local search

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4534 An Application of Modified M-out-of-N Bootstrap Method to Heavy-Tailed Distributions

Authors: Hannah F. Opayinka, Adedayo A. Adepoju


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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4533 Kinetic Model to Interpret Whistler Waves in Multicomponent Non-Maxwellian Space Plasmas

Authors: Warda Nasir, M. N. S. Qureshi


Whistler waves are right handed circularly polarized waves and are frequently observed in space plasmas. The Low frequency branch of the Whistler waves having frequencies nearly around 100 Hz, known as Lion roars, are frequently observed in magnetosheath. Another feature of the magnetosheath is the observations of flat top electron distributions with single as well as two electron populations. In the past, lion roars were studied by employing kinetic model using classical bi-Maxwellian distribution function, however, could not be justified both on quantitatively as well as qualitatively grounds. We studied Whistler waves by employing kinetic model using non-Maxwellian distribution function such as the generalized (r,q) distribution function which is the generalized form of kappa and Maxwellian distribution functions by employing kinetic theory with single or two electron populations. We compare our results with the Cluster observations and found good quantitative and qualitative agreement between them. At times when lion roars are observed (not observed) in the data and bi-Maxwellian could not provide the sufficient growth (damping) rates, we showed that when generalized (r,q) distribution function is employed, the resulted growth (damping) rates exactly match the observations.

Keywords: kinetic model, whistler waves, non-maxwellian distribution function, space plasmas

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4532 The Beta-Fisher Snedecor Distribution with Applications to Cancer Remission Data

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


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

Procedia PDF Downloads 237
4531 Modelling Operational Risk Using Extreme Value Theory and Skew t-Copulas via Bayesian Inference

Authors: Betty Johanna Garzon Rozo, Jonathan Crook, Fernando Moreira


Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation.

Keywords: operational risk, loss distribution approach, extreme value theory, copulas

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4530 Generalized Extreme Value Regression with Binary Dependent Variable: An Application for Predicting Meteorological Drought Probabilities

Authors: Retius Chifurira


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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4529 Extreme Temperature Forecast in Mbonge, Cameroon Through Return Level Analysis of the Generalized Extreme Value (GEV) Distribution

Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph


In this paper, temperature extremes are forecast by employing the block maxima method of the generalized extreme value (GEV) distribution to analyse temperature data from the Cameroon Development Corporation (CDC). By considering two sets of data (raw data and simulated data) and two (stationary and non-stationary) models of the GEV distribution, return levels analysis is carried out and it was found that in the stationary model, the return values are constant over time with the raw data, while in the simulated data the return values show an increasing trend with an upper bound. In the non-stationary model, the return levels of both the raw data and simulated data show an increasing trend with an upper bound. This clearly shows that although temperatures in the tropics show a sign of increase in the future, there is a maximum temperature at which there is no exceedance. The results of this paper are very vital in agricultural and environmental research.

Keywords: forecasting, generalized extreme value (GEV), meteorology, return level

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4528 Pareto System of Optimal Placement and Sizing of Distributed Generation in Radial Distribution Networks Using Particle Swarm Optimization

Authors: Sani M. Lawal, Idris Musa, Aliyu D. Usman


The Pareto approach of optimal solutions in a search space that evolved in multi-objective optimization problems is adopted in this paper, which stands for a set of solutions in the search space. This paper aims at presenting an optimal placement of Distributed Generation (DG) in radial distribution networks with an optimal size for minimization of power loss and voltage deviation as well as maximizing voltage profile of the networks. And these problems are formulated using particle swarm optimization (PSO) as a constraint nonlinear optimization problem with both locations and sizes of DG being continuous. The objective functions adopted are the total active power loss function and voltage deviation function. The multiple nature of the problem, made it necessary to form a multi-objective function in search of the solution that consists of both the DG location and size. The proposed PSO algorithm is used to determine optimal placement and size of DG in a distribution network. The output indicates that PSO algorithm technique shows an edge over other types of search methods due to its effectiveness and computational efficiency. The proposed method is tested on the standard IEEE 34-bus and validated with 33-bus test systems distribution networks. Results indicate that the sizing and location of DG are system dependent and should be optimally selected before installing the distributed generators in the system and also an improvement in the voltage profile and power loss reduction have been achieved.

Keywords: distributed generation, pareto, particle swarm optimization, power loss, voltage deviation

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4527 On the Fractional Integration of Generalized Mittag-Leffler Type Functions

Authors: Christian Lavault


In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

Procedia PDF Downloads 285
4526 Confidence Intervals for Quantiles in the Two-Parameter Exponential Distributions with Type II Censored Data

Authors: Ayman Baklizi


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

Procedia PDF Downloads 317
4525 A Comparative Study of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Extreme Value Theory (EVT) Model in Modeling Value-at-Risk (VaR)

Authors: Longqing Li


The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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4524 Leverage Effect for Volatility with Generalized Laplace Error

Authors: Farrukh Javed, Krzysztof Podgórski


We propose a new model that accounts for the asymmetric response of volatility to positive ('good news') and negative ('bad news') shocks in economic time series the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of 'bad' and 'good' news processes given the past the property that is important for the statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

Keywords: heavy tails, volatility clustering, generalized asymmetric laplace distribution, leverage effect, conditional heteroskedasticity, asymmetric power volatility, GARCH models

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4523 Marginalized Two-Part Joint Models for Generalized Gamma Family of Distributions

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


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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4522 A Novel Guided Search Based Multi-Objective Evolutionary Algorithm

Authors: A. Baviskar, C. Sandeep, K. Shankar


Solving Multi-objective Optimization Problems requires faster convergence and better spread. Though existing Evolutionary Algorithms (EA's) are able to achieve this, the computation effort can further be reduced by hybridizing them with innovative strategies. This study is focuses on converging to the pareto front faster while adapting the advantages of Strength Pareto Evolutionary Algorithm-II (SPEA-II) for a better spread. Two different approaches based on optimizing the objective functions independently are implemented. In the first method, the decision variables corresponding to the optima of individual objective functions are strategically used to guide the search towards the pareto front. In the second method, boundary points of the pareto front are calculated and their decision variables are seeded to the initial population. Both the methods are applied to different constrained and unconstrained multi-objective test functions. It is observed that proposed guided search based algorithm gives better convergence and diversity than several well-known existing algorithms (such as NSGA-II and SPEA-II) in considerably less number of iterations.

Keywords: boundary points, evolutionary algorithms (EA's), guided search, strength pareto evolutionary algorithm-II (SPEA-II)

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