**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**940

# Search results for: Distribution function

##### 940 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.

##### 939 Establishing of Function Point Process Based On Stochastic Distribution

**Authors:**
Do Syung Ryong,
Kang Hyun Su

**Abstract:**

**Keywords:**
Function Point,
Monte Carlo Simulation,
Software
Estimation,
Stochastic Distribution.

##### 938 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.

##### 937 Structural Modelling of the LiCl Aqueous Solution: Using the Hybrid Reverse Monte Carlo (HRMC) Simulation

**Authors:**
M. Habchi,
S.M. Mesli,
M. Kotbi

**Abstract:**

The Reverse Monte Carlo (RMC) simulation is applied in the study of an aqueous electrolyte LiCl6H2O. On the basis of the available experimental neutron scattering data, RMC computes pair radial distribution functions in order to explore the structural features of the system. The obtained results include some unrealistic features. To overcome this problem, we use the Hybrid Reverse Monte Carlo (HRMC), incorporating an energy constraint in addition to the commonly used constraints derived from experimental data. Our results show a good agreement between experimental and computed partial distribution functions (PDFs) as well as a significant improvement in pair partial distribution curves. This kind of study can be considered as a useful test for a defined interaction model for conventional simulation techniques.

**Keywords:**
RMC simulation,
HRMC simulation,
energy
constraint,
screened potential,
glassy state,
liquid state,
partial
distribution function,
pair partial distribution function.

##### 936 Image Compression with Back-Propagation Neural Network using Cumulative Distribution Function

**Authors:**
S. Anna Durai,
E. Anna Saro

**Abstract:**

**Keywords:**
Back-propagation Neural Network,
Cumulative
Distribution Function,
Correlation,
Convergence.

##### 935 Image Mapping with Cumulative Distribution Function for Quick Convergence of Counter Propagation Neural Networks in Image Compression

**Authors:**
S. Anna Durai,
E. Anna Saro

**Abstract:**

**Keywords:**
Correlation,
Counter Propagation Neural Networks,
Cummulative Distribution Function,
Image compression.

##### 934 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.

##### 933 Gold Nanoparticle: Synthesis, Characterization, Clinico-Pathological, Pathological, and Bio-Distribution Studies in Rabbits

**Authors:**
M. M. Bashandy,
A. R. Ahmed,
M. El-Gaffary,
Sahar S. Abd El-Rahman

**Abstract:**

**Keywords:**
Gold nanoparticles,
toxicity,
pathology,
hematology,
liver function,
kidney function.

##### 932 Software Reliability Prediction Model Analysis

**Authors:**
L. Mirtskhulava,
M. Khunjgurua,
N. Lomineishvili,
K. Bakuria

**Abstract:**

Software reliability prediction gives a great opportunity to measure the software failure rate at any point throughout system test. A software reliability prediction model provides with the technique for improving reliability. Software reliability is very important factor for estimating overall system reliability, which depends on the individual component reliabilities. It differs from hardware reliability in that it reflects the design perfection. Main reason of software reliability problems is high complexity of software. Various approaches can be used to improve the reliability of software. We focus on software reliability model in this article, assuming that there is a time redundancy, the value of which (the number of repeated transmission of basic blocks) *can *be an *optimization parameter*. We consider given mathematical model in the assumption that in the system may occur not only irreversible failures, but also a failure that can be taken as self-repairing failures that significantly affect the reliability and accuracy of information transfer. Main task of the given paper is to find a time distribution function (DF) of instructions sequence transmission, which consists of random number of basic blocks. We consider the system software unreliable; the time between adjacent failures has exponential distribution.

**Keywords:**
Exponential distribution,
conditional mean time to failure,
distribution function,
mathematical model,
software reliability.

##### 931 Deformation of Water Waves by Geometric Transitions with Power Law Function Distribution

**Authors:**
E. G. Bautista,
J. M. Reyes,
O. Bautista,
J. C. Arcos

**Abstract:**

In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law distribution. We show that the spatial distribution of the waves in the varying cross-section is a function of a kinematic parameter,κ , and two geometrical parameters εh and w ε . The above spatial behavior of the surface elevation is modeled by an ordinary differential equation. The use of single formulas to model the varying cross sections or transitions considered in this work can be a useful approximation to natural or artificial geometrical configurations.

**Keywords:**
Surface waves,
Asymptotic solution,
Power law
function,
Non-dispersive waves.

##### 930 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.

##### 929 Forecasting for Financial Stock Returns Using a Quantile Function Model

**Authors:**
Yuzhi Cai

**Abstract:**

**Keywords:**
DJIA,
Financial returns,
predictive distribution,
quantile function model.

##### 928 Trimmed Mean as an Adaptive Robust Estimator of a Location Parameter for Weibull Distribution

**Authors:**
Carolina B. Baguio

**Abstract:**

**Keywords:**
Adaptive robust estimate,
asymptotic efficiency,
breakdown point,
influence function,
L-estimates,
location parameter,
tail length,
Weibull distribution.

##### 927 Roll of Membership functions in Fuzzy Logic for Prediction of Shoot Length of Mustard Plant Based on Residual Analysis

**Authors:**
Satyendra Nath Mandal,
J. Pal Choudhury,
Dilip De,
S. R. Bhadra Chaudhuri

**Abstract:**

**Keywords:**
Fuzzification,
defuzzification,
gaussian function,
triangular function,
trapezoidal function,
s-function,
,
membership function,
residual analysis.

##### 926 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.

##### 925 Loss Analysis by Loading Conditions of Distribution Transformers

**Authors:**
A. Bozkurt,
C. Kocatepe,
R. Yumurtaci,
İ. C. Tastan,
G. Tulun

**Abstract:**

**Keywords:**
Distribution system,
distribution transformer,
power
cable,
technical losses.

##### 924 A Novel Probablistic Strategy for Modeling Photovoltaic Based Distributed Generators

**Authors:**
Engy A. Mohamed,
Yasser G. Hegazy

**Abstract:**

**Keywords:**
Comulative distribution function,
distributed
generation,
Monte Carlo.

##### 923 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.

##### 922 Statistical Analysis for Overdispersed Medical Count Data

**Authors:**
Y. N. Phang,
E. F. Loh

**Abstract:**

Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling overdispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling overdispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling overdispered medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling overdispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling overdispersed medical count data when ZIP and ZINB are inadequate.

**Keywords:**
Zero inflated,
inverse trinomial distribution,
Poisson inverse Gaussian distribution,
strict arcsine distribution,
Pearson’s goodness of fit.

##### 921 Texture Observation of Bending by XRD and EBSD Method

**Authors:**
Takashi Sakai,
Yuri Shimomura

**Abstract:**

The crystal orientation is a factor that affects the microscopic material properties. Crystal orientation determines the anisotropy of the polycrystalline material. And it is closely related to the mechanical properties of the material. In this paper, for pure copper polycrystalline material, two different methods; X-Ray Diffraction (XRD) and Electron Backscatter Diffraction (EBSD); and the crystal orientation were analyzed. In the latter method, it is possible that the X-ray beam diameter is thicker as compared to the former, to measure the crystal orientation macroscopically relatively. By measurement of the above, we investigated the change in crystal orientation and internal tissues of pure copper.

**Keywords:**
Bending,
electron backscatter diffraction,
X-ray diffraction,
microstructure,
IPF map,
orientation distribution function.

##### 920 Simplified Models to Determine Nodal Voltagesin Problems of Optimal Allocation of Capacitor Banks in Power Distribution Networks

**Authors:**
A. Pereira,
S. Haffner,
L. V. Gasperin

**Abstract:**

**Keywords:**
Distribution network models,
distribution systems,
optimization,
power system planning.

##### 919 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.

##### 918 Temperature Dependent Interaction Energies among X (=Ru, Rh) Impurities in Pd-Rich PdX Alloys

**Authors:**
M. Asato,
C. Liu,
N. Fujima,
T. Hoshino,
Y. Chen,
T. Mohri

**Abstract:**

We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The *n*-body (*n*=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.

**Keywords:**
Full-potential KKR-Green’s function method,
Fermi-Dirac distribution,
GGA,
phase diagram of Pd-rich PdX (X=Ru,
Rh) alloys,
thermal vibration effect.

##### 917 Forecast Based on an Empirical Probability Function with an Adjusted Error Using Propagation of Error

**Authors:**
Oscar Javier Herrera,
Manuel Ángel Camacho

**Abstract:**

**Keywords:**
Demand Forecasting,
Empirical Distribution,
Propagation of Error.

##### 916 An Effective Approach for Distribution System Power Flow Solution

**Authors:**
A. Alsaadi,
B. Gholami

**Abstract:**

**Keywords:**
Distribution power flow,
distribution automation
system,
radial network,
unbalanced networks.

##### 915 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

##### 914 On the Comparison of Several Goodness of Fit tests under Simple Random Sampling and Ranked Set Sampling

**Authors:**
F. Azna A. Shahabuddin,
Kamarulzaman Ibrahim,
Abdul Aziz Jemain

**Abstract:**

**Keywords:**
Empirical distribution function,
goodness-of-fit,
order statistics,
ranked set sampling

##### 913 Alternative Convergence Analysis for a Kind of Singularly Perturbed Boundary Value Problems

**Authors:**
Jiming Yang

**Abstract:**

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

**Keywords:**
Convergence analysis,
green's function,
singularly perturbed,
equi-distribution,
moving mesh.

##### 912 Proposed a Method for Increasing the Delivery Performance in Dynamic Supply Network

**Authors:**
M. Safaei,
M. Seifert,
K. D. Thoben

**Abstract:**

**Keywords:**
Delivery time uncertainty,
Distribution function,
Statistical method,
Supply Network.

##### 911 Function Approximation with Radial Basis Function Neural Networks via FIR Filter

**Authors:**
Kyu Chul Lee,
Sung Hyun Yoo,
Choon Ki Ahn,
Myo Taeg Lim

**Abstract:**

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

**Keywords:**
Extended kalmin filter (EKF),
classification problem,
radial basis function networks (RBFN),
finite impulse response (FIR)filter.