Search results for: Bayes' Formula

Authors: Hong Choon Ong

Abstract:

Naïve Bayes classifiers are simple probabilistic classifiers. Classification extracts patterns by using data file with a set of labeled training examples and is currently one of the most significant areas in data mining. However, Naïve Bayes assumes the independence among the features. Structural learning among the features thus helps in the classification problem. In this study, the use of structural learning in Bayesian Network is proposed to be applied where there are relationships between the features when using the Naïve Bayes. The improvement in the classification using structural learning is shown if there exist relationship between the features or when they are not independent.

Keywords: Bayesian Network, Classification, Naïve Bayes, Structural Learning.

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Authors: Hadeel Salim Alkutubi

Abstract:

The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.

Keywords: Maximum Likelihood estimation , Bayes estimation, Jeffery prior information, Simulation study

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Authors: Abdullah Y. Al-Hossain

Abstract:

This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley.s approximation to compute the Bayes estimates. Another Bayes estimator has been obtained based on continuous-discrete joint prior for the unknown parameters. An example with the real data is discussed to illustrate the proposed method. Finally, we made comparisons between these estimators and the maximum likelihood estimators using a Monte Carlo simulation study.

Keywords: Progressive type II censoring, compound Rayleigh failure time distribution, maximum likelihood estimation, Bayes estimation, Lindley's approximation method, Monte Carlo simulation.

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Authors: Markus Kaiser, Johannes Buchmann

Abstract:

In this article we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (σ-algebras, probability spaces and conditional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes- Formula. Besides, we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this article shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in cryptographic research, if the corresponding basic mathematical knowledge is available in a database.

Keywords: prime numbers, primality tests, (conditional) probabilitydistributions, formal proof system, higher-order logic, formalverification, Bayes' Formula, Miller-Rabin primality test.

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Authors: Markus Kaiser, Johannes Buchmann

Abstract:

In this paper we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (o--algebras, probability spaces and condi¬tional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes' Formula. Besides we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this paper shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.

Keywords: prime numbers, primality tests, (conditional) proba¬bility distributions, formal proof system, higher-order logic, formal verification, Bayes' Formula, Miller-Rabin primality test.

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Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.

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Authors: Amany M. Alshawi, Khaled Alduhaiman

Abstract:

This paper proposes a technique to protect against email bombing. The technique employs a statistical approach, Naïve Bayes (NB), and Neural Networks to show that it is possible to differentiate between good and bad traffic to protect against email bombing attacks. Neural networks and Naïve Bayes can be trained by utilizing many email messages that include both input and output data for legitimate and non-legitimate emails. The input to the model includes the contents of the body of the messages, the subject, and the headers. This information will be used to determine if the email is normal or an attack email. Preliminary tests suggest that Naïve Bayes can be trained to produce an accurate response to confirm which email represents an attack.

Keywords: Email bombing, Legitimate email, Naïve Bayes, Neural networks, Non-legitimate email.

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Authors: A. Sopharak, B. Uyyanonvara, S. Barman

Abstract:

Diabetic retinopathy is characterized by the development of retinal microaneurysms. The damage can be prevented if disease is treated in its early stages. In this paper, we are comparing Support Vector Machine (SVM) and Naïve Bayes (NB) classifiers for automatic microaneurysm detection in images acquired through non-dilated pupils. The Nearest Neighbor classifier is used as a baseline for comparison. Detected microaneurysms are validated with expert ophthalmologists’ hand-drawn ground-truths. The sensitivity, specificity, precision and accuracy of each method are also compared.

Keywords: Diabetic retinopathy, microaneurysm, Naïve Bayes classifier, SVM classifier.

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Authors: Kefaya Qaddoum

Abstract:

Most of greenhouse growers desire a determined amount of yields in order to accurately meet market requirements. The purpose of this paper is to model a simple but often satisfactory supervised classification method. The original naive Bayes have a serious weakness, which is producing redundant predictors. In this paper, utilized regularization technique was used to obtain a computationally efficient classifier based on naive Bayes. The suggested construction, utilized L1-penalty, is capable of clearing redundant predictors, where a modification of the LARS algorithm is devised to solve this problem, making this method applicable to a wide range of data. In the experimental section, a study conducted to examine the effect of redundant and irrelevant predictors, and test the method on WSG data set for tomato yields, where there are many more predictors than data, and the urge need to predict weekly yield is the goal of this approach. Finally, the modified approach is compared with several naive Bayes variants and other classification algorithms (SVM and kNN), and is shown to be fairly good.

Keywords: Tomato yields prediction, naive Bayes, redundancy

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Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

Abstract:

Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

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Authors: Iman Elyasi, Sadegh Zarmehi

Abstract:

Due to some reasons, observed images are degraded which are mainly caused by noise. Recently image denoising using the wavelet transform has been attracting much attention. Waveletbased approach provides a particularly useful method for image denoising when the preservation of edges in the scene is of importance because the local adaptivity is based explicitly on the values of the wavelet detail coefficients. In this paper, we propose several methods of noise removal from degraded images with Gaussian noise by using adaptive wavelet threshold (Bayes Shrink, Modified Bayes Shrink and Normal Shrink). The proposed thresholds are simple and adaptive to each subband because the parameters required for estimating the threshold depend on subband data. Experimental results show that the proposed thresholds remove noise significantly and preserve the edges in the scene.

Keywords: Image denoising, Bayes Shrink, Modified Bayes Shrink, Normal Shrink.

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Authors: S. Ali Al-Mawsawi, Fadhel A. Albasri

Abstract:

The paper presents a simple and an accurate formula that has been developed for the conduction angle (δ) of a single phase half-wave or full-wave controlled rectifier with RL load. This formula can be also used for calculating the conduction angle (δ) in case of A.C. voltage regulator with inductive load under discontinuous current mode. The simulation results shows that the conduction angle calculated from the developed formula agree very well with that obtained from the exact solution arrived from the iterative method. Applying the developed formula can reduce the computational time and reduce the time for manual classroom calculation. In addition, the proposed formula is attractive for real time implementations.

Keywords: Conduction Angle, Firing Angle, Excitation Angle, Load Angle.

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Authors: Maja Benkovic, Ingrid Bauman

Abstract:

The objective of this work was to investigate flow properties of powdered infant formula samples. Samples were purchased at a local pharmacy and differed in composition. Lactose free infant formula, gluten free infant formula and infant formulas containing dietary fibers and probiotics were tested and compared with a regular infant formula sample which did not contain any of these supplements. Particle size and bulk density were determined and their influence on flow properties was discussed. There were no significant differences in bulk densities of the samples, therefore the connection between flow properties and bulk density could not be determined. Lactose free infant formula showed flow properties different to standard supplement-free sample. Gluten free infant formula with addition of probiotic microorganisms and dietary fiber had the narrowest particle size distribution range and exhibited the best flow properties. All the other samples exhibited the same tendency of decreasing compaction coefficient with increasing flow speed, which means they all become freer flowing with higher flow speeds.

Keywords: flow properties, infant formula, powderedmaterial

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Authors: Homa Torabizadeh

Abstract:

This study proposes a basic molecular formula for all proteins. A total of 10,739 proteins belonging to 9 different protein groups classified on the basis of their functions were selected randomly. They included enzymes, storage proteins, hormones, signalling proteins, structural proteins, transport proteins, immunoglobulins or antibodies, motor proteins and receptor proteins. After obtaining the protein molecular formula using the ProtParam tool, the H/C, N/C, O/C, and S/C ratios were determined for each randomly selected sample. In this case, H, N, O, and S coefficients were specified per carbon atom. Surprisingly, the results demonstrated that H, N, O, and S coefficients for all 10,739 proteins are similar and highly correlated. This study demonstrates that despite differences in the structure and function, all known proteins have a similar basic molecular formula CnH1.58 ± 0.015nN0.28 ± 0.005nO0.30 ± 0.007nS0.01 ± 0.002n. The total correlation between all coefficients was found to be 0.9999.

Keywords: Protein molecular formula, Basic unit formula, Protparam tool.

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Authors: Thanh Nguyen, Andrei Doncescu, Pierre Siegel

Abstract:

Classification is an important data mining technique and could be used as data filtering in artificial intelligence. The broad application of classification for all kind of data leads to be used in nearly every field of our modern life. Classification helps us to put together different items according to the feature items decided as interesting and useful. In this paper, we compare two classification methods Naïve Bayes and ADTree use to detect spam e-mail. This choice is motivated by the fact that Naive Bayes algorithm is based on probability calculus while ADTree algorithm is based on decision tree. The parameter settings of the above classifiers use the maximization of true positive rate and minimization of false positive rate. The experiment results present classification accuracy and cost analysis in view of optimal classifier choice for Spam Detection. It is point out the number of attributes to obtain a tradeoff between number of them and the classification accuracy.

Keywords: Classification, data mining, spam filtering, naive Bayes, decision tree.

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Authors: N. Deetae, S. Sukparungsee, Y. Areepong, K. Jampachaisri

Abstract:

This research is aimed to compare the percentages of correct classification of Empirical Bayes method (EB) to Classical method when data are constructed as near normal, short-tailed and long-tailed symmetric, short-tailed and long-tailed asymmetric. The study is performed using conjugate prior, normal distribution with known mean and unknown variance. The estimated hyper-parameters obtained from EB method are replaced in the posterior predictive probability and used to predict new observations. Data are generated, consisting of training set and test set with the sample sizes 100, 200 and 500 for the binary classification. The results showed that EB method exhibited an improved performance over Classical method in all situations under study.

Keywords: Classification, Empirical Bayes, Posterior predictive probability.

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Authors: Ehab Hasan Ahmed Hasan Ali

Abstract:

The calculation of buckling length factor (K) for steel frames columns is a major and governing processes to determine the dimensions steel frame columns cross sections during design. The buckling length of steel frames columns has a direct effect on the cost (weight) of using cross section. A new formula is required to determine buckling length factor (K) by simplified way. In this research a new formula for buckling length factor (K) was established to determine by accurate method for a limited interval of columns ends rigidity (GA, GB). The new formula can be used ease to evaluate the buckling length factor without needing to complicated equations or difficult charts.

Keywords: Buckling length, New formula, Curve fitting, Simplification, Steel column design.

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Authors: Alhusein Almahjoub, Dongyu Qiu

Abstract:

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

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

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Authors: H. Panahi, S. Asadi

Abstract:

In this paper, the estimation of the stress-strength parameter R = P(Y < X), when X and Y are independent and both are Lomax distributions with the common scale parameters but different shape parameters is studied. The maximum likelihood estimator of R is derived. Assuming that the common scale parameter is known, the bayes estimator and exact confidence interval of R are discussed. Simulation study to investigate performance of the different proposed methods has been carried out.

Keywords: Stress-Strength model; maximum likelihoodestimator; Bayes estimator; Lomax distribution

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Authors: H.Panahi, S.Asadi

Abstract:

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.

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Authors: Danielle Shackley, Yetunde Folajimi

Abstract:

As more people turn to the internet seeking health related information, there is more risk of finding false, inaccurate, or dangerous information. Sentiment analysis is a natural language processing technique that assigns polarity scores of text, ranging from positive, neutral and negative. In this research, we evaluate the weight of a sentiment analysis feature added to fake health news classification models. The dataset consists of existing reliably labeled health article headlines that were supplemented with health information collected about COVID-19 from social media sources. We started with data preprocessing, tested out various vectorization methods such as Count and TFIDF vectorization. We implemented 3 Naive Bayes classifier models, including Bernoulli, Multinomial and Complement. To test the weight of the sentiment analysis feature on the dataset, we created benchmark Naive Bayes classification models without sentiment analysis, and those same models were reproduced and the feature was added. We evaluated using the precision and accuracy scores. The Bernoulli initial model performed with 90% precision and 75.2% accuracy, while the model supplemented with sentiment labels performed with 90.4% precision and stayed constant at 75.2% accuracy. Our results show that the addition of sentiment analysis did not improve model precision by a wide margin; while there was no evidence of improvement in accuracy, we had a 1.9% improvement margin of the precision score with the Complement model. Future expansion of this work could include replicating the experiment process, and substituting the Naive Bayes for a deep learning neural network model.

Keywords: Sentiment analysis, Naive Bayes model, natural language processing, topic analysis, fake health news classification model.

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Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: K. J. Kachiashvili

Abstract:

The Comparison analysis of the Wald-s and Bayestype sequential methods for testing hypotheses is offered. The merits of the new sequential test are: universality which consists in optimality (with given criteria) and uniformity of decision-making regions for any number of hypotheses; simplicity, convenience and uniformity of the algorithms of their realization; reliability of the obtained results and an opportunity of providing the errors probabilities of desirable values. There are given the Computation results of concrete examples which confirm the above-stated characteristics of the new method and characterize the considered methods in regard to each other.

Keywords: Errors of types I and II, likelihood ratio, the Bayes Type Sequential test, the Wald's sequential test, averaged number of observations.

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Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

Abstract:

In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

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Authors: Václav Sadílek, Miroslav Vořechovský

Abstract:

The paper deals with the classical fiber bundle model of equal load sharing, sometimes referred to as the Daniels’ bundle or the democratic bundle. Daniels formulated a multidimensional integral and also a recursive formula for evaluation of the strength cumulative distribution function. This paper describes three algorithms for evaluation of the recursive formula and also their implementations with source codes in the Python high-level programming language. A comparison of the algorithms are provided with respect to execution time. Analysis of orders of magnitudes of addends in the recursion is also provided.

Keywords: Daniels bundle model, equal load sharing, Python, mpmath.

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Authors: Tanawat Limwathanagura, Chartree Sithananun, Teekayu Limchamroon, Thanyarat Singhanart

Abstract:

The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.

Keywords: Space Frame, Student Formula, Torsional Stiffness, TSAE Auto Challenge

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Authors: Chartree Sithananun, Teekayu Limchamroon, Tanawat Limwathanagura, Thanyarat Singhanart

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The objective of this paper is to present the development of the frame of Chulalongkorn University team in TSAE Auto Challenge Student Formula and Student Formula SAE Competition of Japan. Chulalongkorn University's SAE team, has established since year 2003, joined many competitions since year 2006 and became the leading team in Thailand. Through these 5 years, space frame was the most selected and developed year by year through six frame designs. In this paper, the discussions on the conceptual design of these frames are introduced, focusing on the mass and torsional stiffness improvement. The torsional stiffness test was performed on the real used frames and the results are compared. It can be seen that the 2010-2011 frame is firstly designed based on the analysis and experiment that considered the required mass and torsional stiffness. From the torsional stiffness results, it can be concluded that the frames were developed including the decreasing of mass and the increasing torsional stiffness by applying many techniques.

Keywords: SAE Student Formula, Space Frame, Torsional Stiffness

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: Explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula.

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

Abstract:

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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