**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4207

# Search results for: Pareto Probability Distribution function.

##### 4207 Estimating of the Renewal Function with Heavy-tailed Claims

**Authors:**
Rassoul Abdelaziz

**Abstract:**

We develop a new estimator of the renewal function for heavy-tailed claims amounts. Our approach is based on the peak over threshold method for estimating the tail of the distribution with a generalized Pareto distribution. The asymptotic normality of an appropriately centered and normalized estimator is established, and its performance illustrated in a simulation study.

**Keywords:**
Renewal function,
peak-over-threshold,
POT method,
extremes value,
generalized pareto distribution,
heavy-tailed distribution.

##### 4206 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.

##### 4205 Probability Distribution of Rainfall Depth at Hourly Time-Scale

**Authors:**
S. Dan'azumi,
S. Shamsudin,
A. A. Rahman

**Abstract:**

**Keywords:**
Goodness-of-fit test,
Hourly rainfall,
Malaysia,
Probability distribution.

##### 4204 A New Algorithm for Enhanced Robustness of Copyright Mark

**Authors:**
Harsh Vikram Singh,
S. P. Singh,
Anand Mohan

**Abstract:**

This paper discusses a new heavy tailed distribution based data hiding into discrete cosine transform (DCT) coefficients of image, which provides statistical security as well as robustness against steganalysis attacks. Unlike other data hiding algorithms, the proposed technique does not introduce much effect in the stegoimage-s DCT coefficient probability plots, thus making the presence of hidden data statistically undetectable. In addition the proposed method does not compromise on hiding capacity. When compared to the generic block DCT based data-hiding scheme, our method found more robust against a variety of image manipulating attacks such as filtering, blurring, JPEG compression etc.

**Keywords:**
Information Security,
Robust Steganography,
Steganalysis,
Pareto Probability Distribution function.

##### 4203 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.

##### 4202 Easy-Interactive Ordering of the Pareto Optimal Set with Imprecise Weights

**Authors:**
Maria Kalinina,
Aron Larsson,
Leif Olsson

**Abstract:**

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper, is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the reference point may be adjusted to represent the preferences of a decision making agent. Preference information about objective weights from a decision maker may be expressed imprecisely. The developed elicitation procedure provides an opportunity to obtain surrogate numerical weights for the objectives, and thus, to manage impreciseness of preference. The proposed method is a scalable to many objectives and can be used independently or as complementary to the various visualization techniques in the multidimensional case.

**Keywords:**
Imprecise weights,
Multiple objectives,
Pareto
optimality,
Visualization.

##### 4201 Optimum Stratiﬁcation of a Skewed Population

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

**Abstract:**

The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

**Keywords:**
Stratiﬁed sampling,
Optimum strata boundaries,
Optimum sample size,
Pareto distribution,
Mathematical
programming problem,
Dynamic programming technique.

##### 4200 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.

##### 4199 A New Approach for Network Reconfiguration Problem in Order to Deviation Bus Voltage Minimization with Regard to Probabilistic Load Model and DGs

**Authors:**
Mahmood Reza Shakarami,
Reza Sedaghati

**Abstract:**

Recently, distributed generation technologies have received much attention for the potential energy savings and reliability assurances that might be achieved as a result of their widespread adoption. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering wind turbines. The main objective of the DFR is to minimize the deviation of the bus voltage. Since the DFR is a nonlinear optimization problem, we apply the Adaptive Modified Firefly Optimization (AMFO) approach to solve it. As a result of the conflicting behavior of the single- objective function, a fuzzy based clustering technique is employed to reach the set of optimal solutions called Pareto solutions. The approach is tested on the IEEE 32-bus standard test system.

**Keywords:**
Adaptive Modified Firefly Optimization (AMFO),
Pareto solutions,
feeder reconfiguration,
wind turbines,
bus voltage.

##### 4198 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.

##### 4197 Evaluation of Best-Fit Probability Distribution for Prediction of Extreme Hydrologic Phenomena

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

**Abstract:**

The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.

**Keywords:**
Karkheh river,
log pearson type III,
probability distribution,
residual sum of squares.

##### 4196 The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances

**Authors:**
Arkady Bolotin

**Abstract:**

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

##### 4195 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.

##### 4194 Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss

**Authors:**
H. Bevrani,
N. Najafi

**Abstract:**

**Keywords:**
Bayesian inference,
Beta-binomial Distribution,
LPLcriteria,
quadratic loss function.

##### 4193 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

##### 4192 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.

##### 4191 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

##### 4190 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.

##### 4189 A Utilitarian Approach to Modeling Information Flows in Social Networks

**Authors:**
Usha Sridhar,
Sridhar Mandyam

**Abstract:**

**Keywords:**
Borch's Theorem ,
Economic value of information,
Information Exchange,
Pareto Optimal Solution,
Social Networks,
Utility Functions

##### 4188 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.

##### 4187 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

##### 4186 Multi-Objective Random Drift Particle Swarm Optimization Algorithm Based on RDPSO and Crowding Distance Sorting

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

**Abstract:**

**Keywords:**
Multi-objective optimization,
random drift particle
swarm optimization,
crowding distance,
Pareto optimal solution.

##### 4185 Probability of Globality

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

**Abstract:**

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

##### 4184 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.

##### 4183 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.

##### 4182 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.

##### 4181 Determining the Best Fitting Distributions for Minimum Flows of Streams in Gediz Basin

**Authors:**
Naci Büyükkaracığan

**Abstract:**

Today, the need for water sources is swiftly increasing due to population growth. At the same time, it is known that some regions will face with shortage of water and drought because of the global warming and climate change. In this context, evaluation and analysis of hydrological data such as the observed trends, drought and flood prediction of short term flow has great deal of importance. The most accurate selection probability distribution is important to describe the low flow statistics for the studies related to drought analysis. As in many basins In Turkey, Gediz River basin will be affected enough by the drought and will decrease the amount of used water. The aim of this study is to derive appropriate probability distributions for frequency analysis of annual minimum flows at 6 gauging stations of the Gediz Basin. After applying 10 different probability distributions, six different parameter estimation methods and 3 fitness test, the Pearson 3 distribution and general extreme values distributions were found to give optimal results.

**Keywords:**
Gediz Basin,
goodness-of-fit tests,
Minimum flows,
probability distribution.

##### 4180 A Note on Negative Hypergeometric Distribution and Its Approximation

**Authors:**
S. B. Mansuri

**Abstract:**

**Keywords:**
Negative hypergeometric distribution,
Poisson distribution,
Poisson approximation,
Stein-Chen identity,
w-function.

##### 4179 A New Distribution and Application on the Lifetime Data

**Authors:**
Gamze Ozel,
Selen Cakmakyapan

**Abstract:**

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.

**Keywords:**
Marshall-Olkin distribution,
Rayleigh distribution,
estimation,
maximum likelihood.

##### 4178 Nonconforming Control Charts for Zero-Inflated Poisson Distribution

**Authors:**
N. Katemee,
T. Mayureesawan

**Abstract:**

This paper developed the c-Chart based on a Zero- Inflated Poisson (ZIP) processes that approximated by a geometric distribution with parameter p. The p estimated that fit for ZIP distribution used in calculated the mean, median, and variance of geometric distribution for constructed the c-Chart by three difference methods. For cg-Chart, developed c-Chart by used the mean and variance of the geometric distribution constructed control limits. For cmg-Chart, the mean used for constructed the control limits. The cme- Chart, developed control limits of c-Chart from median and variance values of geometric distribution. The performance of charts considered from the Average Run Length and Average Coverage Probability. We found that for an in-control process, the cg-Chart is superior for low level of mean at all level of proportion zero. For an out-of-control process, the cmg-Chart and cme-Chart are the best for mean = 2, 3 and 4 at all level of parameter.

**Keywords:**
average coverage probability,
average run length,
geometric distribution,
zero-inflated poisson distribution