Search results for: generalized order statistics

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Yohei Saika

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On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, multiple interferograms, statistical mechanics

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Authors: Frantisek Mosna

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E-learning has become an efficient and widespread means in process of education at all branches of human activities. Statistics is not an exception. Unfortunately the main focus in the statistics teaching is usually paid to the substitution to formulas. Suitable web-sites can simplify and automate calculation and provide more attention and time to the basic principles of statistics, mathematization of real-life situations and following interpretation of results. We introduce our own web-sites for hypothesis testing. Their didactic aspects, technical possibilities of individual tools for their creating, experience and advantages or disadvantages of them are discussed in this paper. These web-sites do not substitute common statistical software but significantly improve the teaching of the statistics at universities.

Keywords: e-learning, hypothesis testing, PHP, web-sites

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Authors: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

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In this paper, quantitative structure-retention relationships (QSRR) analysis was applied in order to correlate in silico biological and lipophilicity molecular descriptors with retention values for the set of selected s-triazine herbicides. In silico generated biological and lipophilicity descriptors were discriminated using generalized pair correlation method (GPCM). According to this method, the significant difference between independent variables can be noticed regardless almost equal correlation with dependent variable. Using established multiple linear regression (MLR) models some biological characteristics could be predicted. Established MLR models were evaluated statistically and the most suitable models were selected and ranked using sum of ranking differences (SRD) method. In this method, as reference values, average experimentally obtained values are used. Additionally, using SRD method, similarities among investigated s-triazine herbicides can be noticed. These analysis were conducted in order to characterize selected s-triazine herbicides for future investigations regarding their biodegradability. This study is financially supported by COST action TD1305.

Keywords: descriptors, generalized pair correlation method, pesticides, sum of ranking differences

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Authors: Hiba Naccache

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The present research investigated whether gender differences affect performance in a simple math quiz in statistics course. Participants of this study comprised a sample of 567 statistics students in two different universities in Lebanon. Data were collected through a simple math quiz. Analysis of quantitative data indicated that there wasn’t a significant difference in math performance between males and females. The results suggest that improvements in student performance may depend on improved mastery of basic algebra especially for females. The implications of these findings and further recommendations were discussed.

Keywords: gender, education, math, statistics

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Imaneh Abbasi, Ladan Fata, Majid Sadeghi, Sara Banihashemi, Abolfazl Mohammadee

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Background: Dimensional and transdiagnostic approaches as a result of high comorbidity among mental disorders have captured researchers and clinicians interests for exploring the latent factors of development and maintenance of some psychological disorders. The goal of present study is to compare some of these common factors between generalized anxiety disorder and unipolar mood disorder. Methods: 27 patients with generalized anxiety disorder, 29 patients with depression disorder were recruited using SCID-I and 69 non-clinical population were selected using GHQ cut off point. MANCOVA was used for analyzing data. Results: The results show that worry, rumination, intolerance of uncertainty, maladaptive metacognitive beliefs, and experiential avoidance were all significantly different between GAD and unipolar mood disorder groups. However, there were not any significant differences in difficulties in emotion regulation and neuroticism between GAD and unipolar mood disorder groups. Discussion: Results indicate that although there are some transdiagnostic and common factors in GAD and unipolar mood disorder, there may be some specific vulnerability factors for each disorder. Further study is needed for answering these questions.

Keywords: transdiagnostic, depression, generalized anxiety disorder, emotion regulation

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Nada Farhani, Naim Terbeh, Mounir Zrigui

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The recognition of the objects contained in images has always presented a challenge in the field of research because of several difficulties that the researcher can envisage because of the variability of shape, position, contrast of objects, etc. In this paper, we will be interested in the recognition of objects. The classical Hough Transform (HT) presented a tool for detecting straight line segments in images. The technique of HT has been generalized (GHT) for the detection of arbitrary forms. With GHT, the forms sought are not necessarily defined analytically but rather by a particular silhouette. For more precision, we proposed to combine the results from the GHT with the results from a calculation of similarity between the histograms and the spatiograms of the images. The main purpose of our work is to use the concepts from recognition to generate sentences in Arabic that summarize the content of the image.

Keywords: recognition of shape, generalized hough transformation, histogram, spatiogram, learning

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Authors: M. Guemmadi, A. Ouibrahim

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

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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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Authors: Kailash C. Madan

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We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times is compulsory and the second service with general service times is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server must take a vacation of random length of time with general vacation times. We obtain steady state probability generating functions for the queue size as well as the steady state mean queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.

Keywords: batch arrivals, compound Poisson process, generalized Coxian-2 service, steady state

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Authors: Petros Roussos

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The present study focused on students' statistical reasoning related to Null Hypothesis Statistical Testing and p-values. Its objective was to test the hypothesis that neither the place (classroom, at a distance, online) nor the medium that actually supports the learning (ICT, internet, books) has an effect on understanding of statistical concepts. In addition, it was expected that students' attitudes towards statistics would not predict understanding of statistical concepts. The sample consisted of 385 undergraduate and postgraduate students from six state and private universities (five in Greece and one in Cyprus). Students were administered two questionnaires: a) the Greek version of the Survey of Attitudes Toward Statistics, and b) a short instrument which measures students' understanding of statistical significance and p-values. Results suggest that attitudes towards statistics do not predict students' understanding of statistical concepts, whereas the medium did not have an effect.

Keywords: attitudes towards statistics, blended learning, e-learning, statistical reasoning

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Ugiri Ejikeme

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In an executive summary, UNESCO describes Framework for Cultural Statistics as a tool for organizing cultural statistics both nationally and internationally. This is based on conceptual foundation and a common understanding of culture that will enable the measurement of a wide range of cultural expressions. This means therefore that cultural expression in whatever guise has the potentiality of contributing reasonably to the development of a given society. The paper looked into the various tangible and intangible cultures in Imo State of Nigeria. Due to government’s insensitivity, there is need to remind ourselves of the need to pay adequate attention to the cultural heritage bequeathed to us by our forefathers for the sake of posterity. Documenting this information in written form therefore becomes imperative. The study concludes that culture if developed, could reasonably contribute to economic and social growth of the society.

Keywords: detonating culture, statistics and development, Imo State, Nigeria

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Authors: Puttharapong Sakulwaropas, Uraiwan Jaroengeratikun

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Casualty insurance business, the optimal premium pricing and adequate cost for an insurance company are important in risk management. Normally, the insurance pure premium can be determined by multiplying the claim frequency with the claim cost. The aim of this research was to study in the application of generalized linear models to select the risk factor for model of claim frequency and claim cost for estimating a pure premium. In this study, the data set was the claim of comprehensive motor insurance, which was provided by one of the insurance company in Thailand. The results of this study found that the risk factors significantly related to pure premium at the 0.05 level consisted of no claim bonus (NCB) and used of the car (Car code).

Keywords: generalized linear models, risk factor, pure premium, regression model

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Authors: Muhammad Sameer Ahmed, Piotr Remlein, Tansal Gucluoglu

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The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

Keywords: free space optics, generalized frequency division multiplexing, weather conditions, gamma gamma distribution

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: A. Ishag Mohamed, A. A. Rabah

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The objective of this research is to develop a generalized correlation for the prediction of thermal conductivity of n-Alkanes and Alkenes. There is a minority of research and lack of correlation for thermal conductivity of liquids in the open literature. The available experimental data are collected covering the groups of n-Alkanes and Alkenes.The data were assumed to correlate to temperature using Filippov correlation. Nonparametric regression of Grace Algorithm was used to develop the generalized correlation model. A spread sheet program based on Microsoft Excel was used to plot and calculate the value of the coefficients. The results obtained were compared with the data that found in Perry's Chemical Engineering Hand Book. The experimental data correlated to the temperature ranged "between" 273.15 to 673.15 K, with R2 = 0.99.The developed correlation reproduced experimental data that which were not included in regression with absolute average percent deviation (AAPD) of less than 7 %. Thus the spread sheet was quite accurate which produces reliable data.

Keywords: N-Alkanes, N-Alkenes, nonparametric, regression

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Authors: Wajdi Mohamed Ratemi

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

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

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Authors: Jose Juan Peña, J. Morales, J. García-Ravelo

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: Abdel-Aziz M. Mohamed, Nermeen Coutry

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Lead time is an important measure of supply chain performance. It impacts both customer satisfactions as well as the total cost of inventory. This paper presents the result of a study on the analysis of the customer order lead-time for a multinational company. In the study, the lead time was divided into three stages: order entry, order fulfillment, and order delivery. A sample of size 2,425 order lines from the company records were considered for this study. The sample data includes information regarding customer orders from the time of order entry until order delivery. Data regarding the lead time of each sage for different orders were also provided. Summary statistics on lead time data reveals that about 30% of the orders were delivered after the scheduled due date. The result of the multiple linear regression analysis technique revealed that component type, logistics parameter, order size and the customer type have significant impact on lead time. Data analysis on the stages of lead time indicates that stage 2 consumes over 50% of the lead time. Pareto analysis was made to study the reasons for the customer order delay in each of the 3 stages. Recommendation was given to resolve the problem.

Keywords: lead time reduction, customer satisfaction, service quality, statistical analysis

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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Authors: Sara Kanzi, Izzet Sakalli

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The effect of Lorentz symmetry breaking (LSB) on the Hawking radiation of Schwarzschild-like black hole found in the bumblebee gravity model (SBHBGM) is studied in the framework of quantum gravity. To this end, we consider Hawking radiation spin-0 (bosons) and spin-12particles (fermions), which go in and out through the event horizon of the SBHBGM. We use the modified Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and LSB. In particular, we reveal that independent of the spin of the emitted particles, GUP causes a change in the Hawking temperature of the SBHBGM. Furthermore, we compute the semi-analytic greybody factors (for both bosons and fermions) of the SBHBGM. Thus, we reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor. Our findings are graphically depicted.

Keywords: bumblebee gravity model, Hawking radiation, generalized uncertainty principle, Lorentz symmetry breaking

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Authors: Paul R Armstrong

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Doubled haploids (DHs) have become an important breeding tool for creating maize inbred lines, although several bottlenecks in the DH production process limit wider development, application, and adoption of the technique. DH kernels are typically sorted manually and represent about 10% of the seeds in a much larger pool where the remaining 90% are hybrid siblings. This introduces time constraints on DH production and manual sorting is often not accurate. Automated sorting based on the chemical composition of the kernel can be effective, but devices, namely NMR, have not achieved the sorting speed to be a cost-effective replacement to manual sorting. This study evaluated a single kernel near-infrared reflectance spectroscopy (skNIR) platform to accurately identify DH kernels based on oil content. The skNIR platform is a higher-throughput device, approximately 3 seeds/s, that uses spectra to predict oil content of each kernel from maize crosses intentionally developed to create larger than normal oil differences, 1.5%-2%, between DH and hybrid kernels. Spectra from the skNIR were used to construct a partial least squares regression (PLS) model for oil and for a categorical reference model of 1 (DH kernel) or 2 (hybrid kernel) and then used to sort several crosses to evaluate performance. Two approaches were used for sorting. The first used a general PLS model developed from all crosses to predict oil content and then used for sorting each induction cross, the second was the development of a specific model from a single induction cross where approximately fifty DH and one hundred hybrid kernels used. This second approach used a categorical reference value of 1 and 2, instead of oil content, for the PLS model and kernels selected for the calibration set were manually referenced based on traditional commercial methods using coloration of the tip cap and germ areas. The generalized PLS oil model statistics were R2 = 0.94 and RMSE = .93% for kernels spanning an oil content of 2.7% to 19.3%. Sorting by this model resulted in extracting 55% to 85% of haploid kernels from the four induction crosses. Using the second method of generating a model for each cross yielded model statistics ranging from R2s = 0.96 to 0.98 and RMSEs from 0.08 to 0.10. Sorting in this case resulted in 100% correct classification but required models that were cross. In summary, the first generalized model oil method could be used to sort a significant number of kernels from a kernel pool but was not close to the accuracy of developing a sorting model from a single cross. The penalty for the second method is that a PLS model would need to be developed for each individual cross. In conclusion both methods could find useful application in the sorting of DH from hybrid kernels.

Keywords: NIR, haploids, maize, sorting

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Authors: H. R. Fazlollahi

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Dark Energy origin is unknown and so describing this mysterious component in large scale structure needs to manipulate our theories in general relativity. Although in most models, dark energy arises from extra terms through modifying Einstein-Hilbert action, maybe its origin traces back to fundamental aspects of ground energy of space-time given in quantum mechanics. Hence, diluting space-time in general relativity with quantum mechanics properties leads to the Karolyhazy relation corresponding energy density of quantum fluctuations of space-time. Through generalized uncertainty principle and an eye to Karolyhazy approach in this study we extend energy density of quantum fluctuations of space-time. Also, the application of this idea is considered in late time evolution and we have shown how extra term in generalized uncertainty principle plays as a plausible interaction term role in suggested model.

Keywords: generalized uncertainty principle, karolyhazy approach, agegraphic dark energy, cosmology

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Authors: Jose Francisco Ferreira Ribeiro, Alexandre Bevilacqua Leoneti, Andre Lucirton Costa

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This paper presents a mathematical model in binary variables 0/1 to make the assignment of surgical procedures to the operating rooms in a hospital. The proposed mathematical model is based on the generalized assignment problem, which maximizes the sum of preferences for the use of the operating rooms by doctors, respecting the time available in each room. The corresponding program was written in Visual Basic of Microsoft Excel, and tested to schedule surgeries at St. Lydia Hospital in Ribeirao Preto, Brazil.

Keywords: generalized assignment problem, logistics, optimization, scheduling

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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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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Authors: Farrukh Javed, Krzysztof Podgórski

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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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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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