**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**555

# Search results for: ruin probability

##### 555 Ruin Probability for a Markovian Risk Model with Two-type Claims

**Authors:**
Dongdong Zhang,
Deran Zhang

**Abstract:**

In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

**Keywords:**
Risk model,
ruin probability,
Markov jump process,
integral equation.

##### 554 Ruin Probabilities with Dependent Rates of Interest and Autoregressive Moving Average Structures

**Authors:**
Fenglong Guo,
Dingcheng Wang

**Abstract:**

**Keywords:**
Lundberg inequality,
NWUC,
Renewal recursive technique,
Ruin probability

##### 553 A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes

**Authors:**
Amir T. Payandeh Najafabadi

**Abstract:**

**Keywords:**
Ruin probability,
compound Poisson processes,
mixture exponential (hyperexponential) distribution,
heavy-tailed
distributions.

##### 552 Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model

**Authors:**
Zina Benouaret,
Djamil Aissani

**Abstract:**

**Keywords:**
Markov chain,
risk models,
ruin probabilities,
strong
stability analysis.

##### 551 The Study of the Discrete Risk Model with Random Income

**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.

##### 550 Performance of the Strong Stability Method in the Univariate Classical Risk Model

**Authors:**
Safia Hocine,
Zina Benouaret,
Djamil A¨ıssani

**Abstract:**

**Keywords:**
Markov Chain,
regenerative processes,
risk models,
ruin probability,
strong stability.

##### 549 The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances

**Authors:**
Arkady Bolotin

**Abstract:**

**Keywords:**
Possibility distributions,
possibility-probability relationship.

##### 548 An Overview of Handoff Techniques in Cellular Networks

**Authors:**
Nasıf Ekiz,
Tara Salih,
Sibel Küçüköner,
Kemal Fidanboylu

**Abstract:**

Continuation of an active call is one of the most important quality measurements in the cellular systems. Handoff process enables a cellular system to provide such a facility by transferring an active call from one cell to another. Different approaches are proposed and applied in order to achieve better handoff service. The principal parameters used to evaluate handoff techniques are: forced termination probability and call blocking probability. The mechanisms such as guard channels and queuing handoff calls decrease the forced termination probability while increasing the call blocking probability. In this paper we present an overview about the issues related to handoff initiation and decision and discuss about different types of handoff techniques available in the literature.

**Keywords:**
Handoff,
Forced Termination Probability,
Blocking probability,
Handoff Initiation,
Handoff Decision,
Handoff Prioritization Schemes.

##### 547 Computation of Probability Coefficients using Binary Decision Diagram and their Application in Test Vector Generation

**Authors:**
Ashutosh Kumar Singh,
Anand Mohan

**Abstract:**

**Keywords:**
Binary Decision Diagrams,
Spectral Coefficients,
Fault detection

##### 546 Determination of Sensitive Transmission Lines Due to the Effect of Protection System Hidden Failure in a Critical System Cascading Collapse

**Authors:**
N. A. Salim,
M. M. Othman,
I. Musirin,
M. S. Serwan

**Abstract:**

Protection system hidden failures have been identified as one of the main causes of system cascading collapse resulting to power system instability. In this paper, a systematic approach is presented in order to identify the probability of a system cascading collapse by taking into consideration the effect of protection system hidden failure. This includes the accurate calculation of the probability of hidden failure as it will provide significant impinge on the findings of the probability of system cascading collapse. The probability of a system cascading collapse is then used to identify the initial tripping of sensitive transmission lines which will contribute to a critical system cascading collapse. Based on the results obtained from this study, it is important to decide on the accurate value of the hidden failure probability as it will affect the probability of a system cascading collapse.

**Keywords:**
Critical system cascading collapse,
hidden failure,
probability of cascading collapse,
sensitive transmission lines.

##### 545 An Approaching Index to Evaluate a forward Collision Probability

**Authors:**
Yuan-Lin Chen

**Abstract:**

This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

**Keywords:**
Approaching index,
forward collision probability,
time to collision,
time headway.

##### 544 Application of Adaptive Genetic Algorithm in Function Optimization

**Authors:**
Panpan Xu,
Shulin Sui

**Abstract:**

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

**Keywords:**
Genetic algorithm,
Adaptive genetic algorithm,
Function optimization.

##### 543 Determination of the Best Fit Probability Distribution for Annual Rainfall in Karkheh River at Iran

**Authors:**
Karim Hamidi Machekposhti,
Hossein Sedghi

**Abstract:**

This study was designed to find the best-fit probability distribution of annual rainfall based on 50 years sample (1966-2015) in the Karkheh river basin at Iran using six probability distributions: Normal, 2-Parameter Log Normal, 3-Parameter Log Normal, Pearson Type 3, Log Pearson Type 3 and Gumbel distribution. The best fit probability distribution was selected using Stormwater Management and Design Aid (SMADA) software and based on the Residual Sum of Squares (R.S.S) between observed and estimated values Based on the R.S.S values of fit tests, the Log Pearson Type 3 and then Pearson Type 3 distributions were found to be the best-fit probability distribution at the Jelogir Majin and Pole Zal rainfall gauging station. The annual values of expected rainfall were calculated using the best fit probability distributions and can be used by hydrologists and design engineers in future research at studied region and other region in the world.

**Keywords:**
Log Pearson Type 3,
SMADA,
rainfall,
Karkheh River.

##### 542 A Case Study on the Numerical-Probability Approach for Deep Excavation Analysis

**Authors:**
Komeil Valipourian

**Abstract:**

Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

**Keywords:**
Numerical probability modeling,
deep excavation,
allowable maximum displacement,
finite difference method,
FDM.

##### 541 Probability of Globality

**Authors:**
Eva Eggeling,
Dieter W. Fellner,
Torsten Ullrich

**Abstract:**

**Keywords:**
global optimization,
probability theory,
probability of
globality

##### 540 Approximation for Average Error Probability of BPSK in the Presence of Phase Error

**Authors:**
Yeonsoo Jang,
Dongweon Yoon,
Ki Ho Kwon,
Jaeyoon Lee,
Wooju Lee

**Abstract:**

**Keywords:**
Average error probability,
Phase shift keying,
Phase
error

##### 539 The Giant Component in a Random Subgraph of a Weak Expander

**Authors:**
Yilun Shang

**Abstract:**

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

**Keywords:**
subgraph,
expander,
random graph,
giant component,
percolation.

##### 538 The Locker Problem with Empty Lockers

**Authors:**
David Avis,
Luc Devroye,
Kazuo Iwama

**Abstract:**

We consider a cooperative game played by n players against a referee. The players names are randomly distributed among n lockers, with one name per locker. Each player can open up to half the lockers and each player must find his name. Once the game starts the players may not communicate. It has been previously shown that, quite surprisingly, an optimal strategy exists for which the success probability is never worse than 1 − ln 2 ≈ 0.306. In this paper we consider an extension where the number of lockers is greater than the number of players, so that some lockers are empty. We show that the players may still win with positive probability even if there are a constant k number of empty lockers. We show that for each fixed probability p, there is a constant c so that the players can win with probability at least p if they are allowed to open cn lockers.

**Keywords:**
Locker problem,
pointer-following algorithms.

##### 537 Probabilities and the Persistence of Memory in a Bingo-like Carnival Game

**Authors:**
M. Glomski,
M. Lopes

**Abstract:**

Seemingly simple probabilities in the m-player game bingo have never been calculated. These probabilities include expected game length and the expected number of winners on a given turn. The difficulty in probabilistic analysis lies in the subtle interdependence among the m-many bingo game cards in play. In this paper, the game i got it!, a bingo variant, is considered. This variation provides enough weakening of the inter-player dependence to allow probabilistic analysis not possible for traditional bingo. The probability of winning in exactly k turns is calculated for a one-player game. Given a game of m-many players, the expected game length and tie probability are calculated. With these calculations, the game-s interesting payout scheme is considered.

**Keywords:**
Conditional probability,
games of chance,
npersongames,
probability theory.

##### 536 Simple Procedure for Probability Calculation of Tensile Crack Occurring in Rigid Pavement – Case Study

**Authors:**
Aleš Florian,
Lenka Ševelová,
Jaroslav Žák

**Abstract:**

Formation of tensile cracks in concrete slabs of rigid pavement can be (among others) the initiation point of the other, more serious failures which can ultimately lead to complete degradation of the concrete slab and thus the whole pavement. Two measures can be used for reliability assessment of this phenomenon - the probability of failure and/or the reliability index. Different methods can be used for their calculation. The simple ones are called moment methods and simulation techniques. Two methods - FOSM Method and Simple Random Sampling Method - are verified and their comparison is performed. The influence of information about the probability distribution and the statistical parameters of input variables as well as of the limit state function on the calculated reliability index and failure probability are studied in three points on the lower surface of concrete slabs of the older type of rigid pavement formerly used in the Czech Republic.

**Keywords:**
Failure,
pavement,
probability,
reliability index,
simulation,
tensile crack.

##### 535 Detection of Bias in GPS satellites- Measurements for Enhanced Measurement Integrity

**Authors:**
Mamoun F. Abdel-Hafez

**Abstract:**

In this paper, the detection of a fault in the Global Positioning System (GPS) measurement is addressed. The class of faults considered is a bias in the GPS pseudorange measurements. This bias is modeled as an unknown constant. The fault could be the result of a receiver fault or signal fault such as multipath error. A bias bank is constructed based on set of possible fault hypotheses. Initially, there is equal probability of occurrence for any of the biases in the bank. Subsequently, as the measurements are processed, the probability of occurrence for each of the biases is sequentially updated. The fault with a probability approaching unity will be declared as the current fault in the GPS measurement. The residual formed from the GPS and Inertial Measurement Unit (IMU) measurements is used to update the probability of each fault. Results will be presented to show the performance of the presented algorithm.

**Keywords:**
Estimation and filtering,
Statistical data analysis,
Faultdetection and identification.

##### 534 One scheme of Transition Probability Evaluation

**Authors:**
Alexander B. Bichkov,
Alla A. Mityureva,
Valery V. Smirnov

**Abstract:**

**Keywords:**
Path integral,
saddle point method,
semiclassical approximation,
transition probability

##### 533 System Overflow/Blocking Transients For Queues with Batch Arrivals Using a Family of Polynomials Resembling Chebyshev Polynomials

**Authors:**
Vitalice K. Oduol,
C. Ardil

**Abstract:**

The paper shows that in the analysis of a queuing system with fixed-size batch arrivals, there emerges a set of polynomials which are a generalization of Chebyshev polynomials of the second kind. The paper uses these polynomials in assessing the transient behaviour of the overflow (equivalently call blocking) probability in the system. A key figure to note is the proportion of the overflow (or blocking) probability resident in the transient component, which is shown in the results to be more significant at the beginning of the transient and naturally decays to zero in the limit of large t. The results also show that the significance of transients is more pronounced in cases of lighter loads, but lasts longer for heavier loads.

**Keywords:**
batch arrivals,
blocking probability,
generalizedChebyshev polynomials,
overflow probability,
queue transientanalysis

##### 532 A Computer Model of Quantum Field Theory

**Authors:**
Hans H. Diel

**Abstract:**

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

**Keywords:**
Computational Modeling,
Simulation of Quantum Theory,
Quantum Field Theory,
Quantum Electrodynamics

##### 531 Effect of Specimen Thickness on Probability Distribution of Grown Crack Size in Magnesium Alloys

**Authors:**
Seon Soon Choi

**Abstract:**

The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

**Keywords:**
Crack size,
Fatigue crack propagation,
Magnesium alloys,
Probability distribution,
Specimen thickness.

##### 530 Daily Probability Model of Storm Events in Peninsular Malaysia

**Authors:**
Mohd Aftar Abu Bakar,
Noratiqah Mohd Ariff,
Abdul Aziz Jemain

**Abstract:**

Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.

**Keywords:**
Daily probability model,
monsoon seasons,
regions,
storm events.

##### 529 Effect of Load Ratio on Probability Distribution of Fatigue Crack Propagation Life in Magnesium Alloys

**Authors:**
Seon Soon Choi

**Abstract:**

**Keywords:**
Load ratio,
fatigue crack propagation life,
Magnesium alloys,
probability distribution.

##### 528 Probability-Based Damage Detection of Structures Using Kriging Surrogates and Enhanced Ideal Gas Molecular Movement Algorithm

**Authors:**
M. R. Ghasemi,
R. Ghiasi,
H. Varaee

**Abstract:**

Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.

**Keywords:**
Enhanced ideal gas molecular movement,
Kriging,
probability-based damage detection,
probability of damage existence,
surrogate modeling,
uncertainty quantification.

##### 527 Stochastic Repair and Replacement with a Single Repair Channel

**Authors:**
Mohammed A. Hajeeh

**Abstract:**

**Keywords:**
Repairable models,
imperfect,
availability,
exponential distribution.

##### 526 Conservativeness of Probabilistic Constrained Optimal Control Method for Unknown Probability Distribution

**Authors:**
Tomoaki Hashimoto

**Abstract:**

**Keywords:**
Optimal control,
stochastic systems,
discrete-time
systems,
probabilistic constraints.