**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3355

# Search results for: Probability Density Function

##### 3355 An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory

**Authors:**
R. K. Saxena,
Ravi Saxena

**Abstract:**

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

**Keywords:**
Fox-Wright function,
Inverse Gaussian distribution,
Krtzel function & Bessel function of the third kind.

##### 3354 Improved Segmentation of Speckled Images Using an Arithmetic-to-Geometric Mean Ratio Kernel

**Abstract:**

**Keywords:**
Discriminant function,
false alarm,
segmentation,
signal-to-noise ratio,
skewness,
speckle.

##### 3353 Probability Density Estimation Using Advanced Support Vector Machines and the Expectation Maximization Algorithm

**Authors:**
Refaat M Mohamed,
Ayman El-Baz,
Aly A. Farag

**Abstract:**

This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.

**Keywords:**
Density Estimation,
SVM,
Learning Algorithms,
Parameters Estimation.

##### 3352 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.

##### 3351 A Stochastic Approach to Extreme Wind Speeds Conditions on a Small Axial Wind Turbine

**Authors:**
Nkongho Ayuketang Arreyndip,
Ebobenow Joseph

**Abstract:**

**Keywords:**
Probability,
Stochastic,
Probability density function,
Turbulence.

##### 3350 Stochastic Risk Analysis Framework for Building Construction Projects

**Authors:**
Abdulkadir Abu Lawal

**Abstract:**

The study was carried out to establish the probability density function of some selected building construction projects of similar complexity delivered using Bill of Quantities (BQ) and Lump Sum (LS) forms of contract, and to draw a reliability scenario for each form of contract. 30 of such delivered projects are analyzed for each of the contract forms using Weibull Analysis, and their Weibull functions (α, and β) are determined based on their completion times. For the BQ form of contract delivered projects, α is calculated as 1.6737E20 and β as + 0.0115 and for the LS form, α is found to be 5.6556E03 and β is determined as + 0.4535. Using these values, respective probability density functions are calculated and plotted, as handy tool for risk analysis of future projects of similar characteristics. By input of variables from other projects, decision making processes can be made for a whole project or its components using EVM Analysis in project evaluation and review techniques. This framework, as a quantitative approach, depends on the assumption of normality in projects completion time, it can help greatly in determining the completion time probability for veritable projects using any of the contract forms under consideration. Projects aspects that are not amenable to measurement, on the other hand, can be analyzed using fuzzy sets and fuzzy logic. This scenario can be drawn for different types of building construction projects, and using different suitable forms of contract in projects delivery.

**Keywords:**
Building construction,
Projects,
Forms of contract,
Probability density function,
Reliability scenario.

##### 3349 The Statistical Properties of Filtered Signals

**Authors:**
Ephraim Gower,
Thato Tsalaile,
Monageng Kgwadi,
Malcolm Hawksford.

**Abstract:**

In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.

**Keywords:**
Circular Convolution,
linear Convolution,
mixture density
function.

##### 3348 A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function

**Authors:**
Meriem Bahij,
Ahmed Nafidi,
Boujemâa Achchab,
Sílvio M. A. Gama,
José A. O. Matos

**Abstract:**

**Keywords:**
Diffusion process,
discrete sampling,
likelihood
estimation method,
simulation,
stochastic diffusion equation,
trends
functions,
bi-parameters Weibull density function.

##### 3347 Reliability Indices Evaluation of SEIG Rotor Core Magnetization with Minimum Capacitive Excitation for WECs

**Authors:**
Lokesh Varshney,
R. K. Saket

**Abstract:**

This paper presents reliability indices evaluation of the rotor core magnetization of the induction motor operated as a self excited induction generator by using probability distribution approach and Monte Carlo simulation. Parallel capacitors with calculated minimum capacitive value across the terminals of the induction motor operated as a SEIG with unregulated shaft speed have been connected during the experimental study. A three phase, 4 poles, 50Hz, 5.5 hp, 12.3A, 230V induction motor coupled with DC Shunt Motor was tested in the electrical machine laboratory with variable reactive loads. Based on this experimental study, it is possible to choose a reliable induction machines operated as a SEIG for unregulated renewable energy application in remote area or where grid is not available. Failure density function, cumulative failure distribution function, survivor function, hazard model, probability of success and probability of failure for reliability evaluation of the three phase induction motor operating as a SEIG have been presented graphically in this paper.

**Keywords:**
Residual magnetism,
magnetization curve,
induction
motor,
self excited induction generator,
probability distribution,
Monte Carlo simulation.

##### 3346 Carbon Disulfide Production via Hydrogen Sulfide Methane Reformation

**Authors:**
H. Hosseini,
M. Javadi,
M. Moghiman,
M. H. Ghodsi Rad

**Abstract:**

**Keywords:**
Carbon disulfide,
sour natural gas,
H2SMR,
probability density function.

##### 3345 Unsupervised Feature Selection Using Feature Density Functions

**Authors:**
Mina Alibeigi,
Sattar Hashemi,
Ali Hamzeh

**Abstract:**

**Keywords:**
Feature,
Feature Selection,
Filter,
Probability
Density Function

##### 3344 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

##### 3343 Probability of Globality

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

**Abstract:**

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

##### 3342 Approximations to the Distribution of the Sample Correlation Coefficient

**Authors:**
John N. Haddad,
Serge B. Provost

**Abstract:**

**Keywords:**
Sample correlation coefficient,
density approximation,
confidence intervals.

##### 3341 Dynamic Economic Dispatch Constrained by Wind Power Weibull Distribution: A Here-and-Now Strategy

**Authors:**
Mostafa A. Elshahed,
Magdy M. Elmarsfawy,
Hussain M. Zain Eldain

**Abstract:**

In this paper, a Dynamic Economic Dispatch (DED) model is developed for the system consisting of both thermal generators and wind turbines. The inclusion of a significant amount of wind energy into power systems has resulted in additional constraints on DED to accommodate the intermittent nature of the output. The probability of stochastic wind power based on the Weibull probability density function is included in the model as a constraint; A Here-and-Now Approach. The Environmental Protection Agency-s hourly emission target, which gives the maximum emission during the day, is used as a constraint to reduce the atmospheric pollution. A 69-bus test system with non-smooth cost function is used to illustrate the effectiveness of the proposed model compared with static economic dispatch model with including the wind power.

**Keywords:**
Dynamic Economic Dispatch,
StochasticOptimization,
Weibull Distribution,
Wind Power

##### 3340 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.

##### 3339 Mobile Robot Path Planning Utilizing Probability Recursive Function

**Authors:**
Ethar H. Khalil,
Bahaa I. Kazem

**Abstract:**

**Keywords:**
Mobile robot,
path planning,
Bezier curve.

##### 3338 Application Reliability Method for Concrete Dams

**Authors:**
Mustapha Kamel Mihoubi,
Mohamed Essadik Kerkar

**Abstract:**

Probabilistic risk analysis models are used to provide a better understanding of the reliability and structural failure of works, including when calculating the stability of large structures to a major risk in the event of an accident or breakdown. This work is interested in the study of the probability of failure of concrete dams through the application of reliability analysis methods including the methods used in engineering. It is in our case, the use of level 2 methods via the study limit state. Hence, the probability of product failures is estimated by analytical methods of the type first order risk method (FORM) and the second order risk method (SORM). By way of comparison, a level three method was used which generates a full analysis of the problem and involves an integration of the probability density function of random variables extended to the field of security using the Monte Carlo simulation method. Taking into account the change in stress following load combinations: normal, exceptional and extreme acting on the dam, calculation of the results obtained have provided acceptable failure probability values which largely corroborate the theory, in fact, the probability of failure tends to increase with increasing load intensities, thus causing a significant decrease in strength, shear forces then induce a shift that threatens the reliability of the structure by intolerable values of the probability of product failures. Especially, in case the increase of uplift in a hypothetical default of the drainage system.

**Keywords:**
Dam,
failure,
limit-state,
Monte Carlo simulation,
reliability,
probability,
simulation,
sliding,
Taylor.

##### 3337 Estimating the Effect of Fluid in Pressing Process

**Authors:**
A. Movaghar,
R. A. Mahdavinejad

**Abstract:**

To analyze the effect of various parameters of fluid on the material properties such as surface and depth defects and/or cracks, it is possible to determine the affection of pressure field on these specifications. Stress tensor analysis is also able to determine the points in which the probability of defection creation is more. Besides, from pressure field, it is possible to analyze the affection of various fluid specifications such as viscosity and density on defect created in the material. In this research, the concerned boundary conditions are analyzed first. Then the solution network and stencil used are mentioned. With the determination of relevant equation on the fluid flow between notch and matrix and their discretion according to the governed boundary conditions, these equations can be solved. Finally, with the variation creations on fluid parameters such as density and viscosity, the affection of these variations can be determined on pressure field. In this direction**,** the flowchart and solution algorithm with their results as vortex and current function contours for two conditions with most applications in pressing process are introduced and discussed.

**Keywords:**
Pressing,
notch,
matrix,
flow function,
vortex.

##### 3336 Modeling of Statistically Multiplexed Non Uniform Activity VBR Video

**Authors:**
J. P. Dubois

**Abstract:**

**Keywords:**
ARMA,
ATM networks,
burstiness,
multimediatraffic,
VBR video.

##### 3335 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

##### 3334 Analysis of Different Combining Schemes of Two Amplify-Forward Relay Branches with Individual Links Experiencing Nakagami Fading

**Authors:**
Babu Sena Paul,
Ratnajit Bhattacharjee

**Abstract:**

Relay based communication has gained considerable importance in the recent years. In this paper we find the end-toend statistics of a two hop non-regenerative relay branch, each hop being Nakagami-m faded. Closed form expressions for the probability density functions of the signal envelope at the output of a selection combiner and a maximal ratio combiner at the destination node are also derived and analytical formulations are verified through computer simulation. These density functions are useful in evaluating the system performance in terms of bit error rate and outage probability.

**Keywords:**
co-operative diversity,
diversity combining,
maximal ratio combining,
selection combining.

##### 3333 Speaker Identification by Joint Statistical Characterization in the Log Gabor Wavelet Domain

**Authors:**
Suman Senapati,
Goutam Saha

**Abstract:**

**Keywords:**
Speaker Identification,
Log Gabor Wavelet,
Bayesian Bivariate Estimator,
Circularly Symmetric Probability
Density Function,
SIRP.

##### 3332 Establishing a Probabilistic Model of Extrapolated Wind Speed Data for Wind Energy Prediction

**Authors:**
Mussa I. Mgwatu,
Reuben R. M. Kainkwa

**Abstract:**

**Keywords:**
Probabilistic models,
wind speed,
wind energy

##### 3331 Performance of Dual MRC Receiver for M-ary Modulations over Correlated Nakagami-m Fading Channels with Non-identical and Arbitrary Fading Parameter

**Authors:**
Rupaban Subadar

**Abstract:**

**Keywords:**
MRC,
correlated Nakagami-m fading,
non-identicalfading statistics,
average symbol error rate

##### 3330 A Study on Mechanical Properties of Fiberboard Made of Durian Rind through Latex with Phenolic Resin as Binding Agent

**Authors:**
W. Wiyaratn,
A. Watanapa

**Abstract:**

**Keywords:**
Durian rind,
latex,
phenolic resin,
medium density
fiberboard

##### 3329 Characteristic Function in Estimation of Probability Distribution Moments

**Authors:**
Vladimir S. Timofeev

**Abstract:**

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

**Keywords:**
Characteristic function,
distributional moments,
robustness,
outlier,
statistical estimation problem,
statistical simulation.

##### 3328 The Impact of Upgrades on ERP System Reliability

**Authors:**
F. Urem,
K. Fertalj,
I. Livaja

**Abstract:**

**Keywords:**
ERP,
upgrade,
reliability,
Weibull model

##### 3327 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.

##### 3326 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.