**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2229

# Search results for: probability distribution

##### 2229 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.

##### 2228 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.

##### 2227 The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances

**Authors:**
Arkady Bolotin

**Abstract:**

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

##### 2226 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.

##### 2225 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.

##### 2224 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.

##### 2223 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.

##### 2222 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.

##### 2221 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

##### 2220 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.

##### 2219 Coverage Probability of Confidence Intervals for the Normal Mean and Variance with Restricted Parameter Space

**Authors:**
Sa-aat Niwitpong

**Abstract:**

Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.

**Keywords:**
Confidence interval,
coverage probability,
expected length,
restricted parameter space.

##### 2218 A Simplified Distribution for Nonlinear Seas

**Authors:**
M. A. Tayfun,
M. A. Alkhalidi

**Abstract:**

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

**Keywords:**
Ocean waves,
probability distributions,
second-order nonlinearities,
skewness coefficient,
wave steepness.

##### 2217 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

##### 2216 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.

##### 2215 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.

##### 2214 Identification of Outliers in Flood Frequency Analysis: Comparison of Original and Multiple Grubbs-Beck Test

**Authors:**
Ayesha S. Rahman,
Khaled Haddad,
Ataur Rahman

**Abstract:**

At-site flood frequency analysis is used to estimate flood quantiles when at-site record length is reasonably long. In Australia, FLIKE software has been introduced for at-site flood frequency analysis. The advantage of FLIKE is that, for a given application, the user can compare a number of most commonly adopted probability distributions and parameter estimation methods relatively quickly using a windows interface. The new version of FLIKE has been incorporated with the multiple Grubbs and Beck test which can identify multiple numbers of potentially influential low flows. This paper presents a case study considering six catchments in eastern Australia which compares two outlier identification tests (original Grubbs and Beck test and multiple Grubbs and Beck test) and two commonly applied probability distributions (Generalized Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE software. It has been found that the multiple Grubbs and Beck test when used with LP3 distribution provides more accurate flood quantile estimates than when LP3 distribution is used with the original Grubbs and Beck test. Between these two methods, the differences in flood quantile estimates have been found to be up to 61% for the six study catchments. It has also been found that GEV distribution (with L moments) and LP3 distribution with the multiple Grubbs and Beck test provide quite similar results in most of the cases; however, a difference up to 38% has been noted for flood quantiles for annual exceedance probability (AEP) of 1 in 100 for one catchment. This finding needs to be confirmed with a greater number of stations across other Australian states.

**Keywords:**
Floods,
FLIKE,
probability distributions,
flood
frequency,
outlier.

##### 2213 A Statistical Model for the Dynamics of Single Cathode Spot in Vacuum Cylindrical Cathode

**Authors:**
Po-Wen Chen,
Jin-Yu Wu,
Md. Manirul Ali,
Yang Peng,
Chen-Te Chang,
Der-Jun Jan

**Abstract:**

**Keywords:**
Cathode spot,
vacuum arc discharge,
transverse
magnetic field,
random walk.

##### 2212 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.

##### 2211 Stochastic Repair and Replacement with a Single Repair Channel

**Authors:**
Mohammed A. Hajeeh

**Abstract:**

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

##### 2210 Influence of Maximum Fatigue Load on Probabilistic Aspect of Fatigue Crack Propagation Life at Specified Grown Crack in Magnesium Alloys

**Authors:**
Seon Soon Choi

**Abstract:**

**Keywords:**
Fatigue crack propagation life,
magnesium alloys,
maximum fatigue load,
probability.

##### 2209 Entropic Measures of a Probability Sample Space and Exponential Type (α, β) Entropy

**Authors:**
Rajkumar Verma,
Bhu Dev Sharma

**Abstract:**

Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon’s entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon’s and those other entropy generalizations that involve logarithmic function for a probability distribution in general. In this paper, we introduce a measure of sample space, called ‘entropic measure of a sample space’, with respect to the underlying distribution. It is shown in both discrete and continuous cases that this new measure depends on the parameters of the distribution on the sample space - same sample space having different ‘entropic measures’ depending on the distributions defined on it. It was noted that Campbell’s idea applied for R`enyi’s parametric entropy of a given order also. Knowing that parameters play a role in providing suitable choices and extended applications, paper studies parametric entropic measures of sample spaces also. Exponential entropies related to Shannon’s and those generalizations that have logarithmic functions, i.e. are additive have been studies for wider understanding and applications. We propose and study exponential entropies corresponding to non additive entropies of type (α, β), which include Havard and Charvˆat entropy as a special case.

**Keywords:**
Sample space,
Probability distributions,
Shannon’s entropy,
R`enyi’s entropy,
Non-additive entropies .

##### 2208 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.

##### 2207 Steering Velocity Bounded Mobile Robots in Environments with Partially Known Obstacles

**Authors:**
Reza Hossseynie,
Amir Jafari

**Abstract:**

**Keywords:**
Steering,
obstacle avoidance,
mobile robots,
constrained directions control,
artificial potential field.

##### 2206 The Research and Application of M/M/1/N Queuing Model with Variable Input Rates, Variable Service Rates and Impatient Customers

**Authors:**
Quanru Pan

**Abstract:**

**Keywords:**
variable input rates,
impatient customer,
variable servicerates,
profit maximization.

##### 2205 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.

##### 2204 Analytical Slope Stability Analysis Based on the Statistical Characterization of Soil Shear Strength

**Authors:**
Bernardo C. P. Albuquerque,
Darym J. F. Campos

**Abstract:**

**Keywords:**
Statistical slope stability analysis,
Skew distributions,
Probability of failure,
Functions of random variables.

##### 2203 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.

##### 2202 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

##### 2201 Modeling Default Probabilities of the Chosen Czech Banks in the Time of the Financial Crisis

**Authors:**
Petr Gurný

**Abstract:**

One of the most important tasks in the risk management is the correct determination of probability of default (PD) of particular financial subjects. In this paper a possibility of determination of financial institution’s PD according to the creditscoring models is discussed. The paper is divided into the two parts. The first part is devoted to the estimation of the three different models (based on the linear discriminant analysis, logit regression and probit regression) from the sample of almost three hundred US commercial banks. Afterwards these models are compared and verified on the control sample with the view to choose the best one. The second part of the paper is aimed at the application of the chosen model on the portfolio of three key Czech banks to estimate their present financial stability. However, it is not less important to be able to estimate the evolution of PD in the future. For this reason, the second task in this paper is to estimate the probability distribution of the future PD for the Czech banks. So, there are sampled randomly the values of particular indicators and estimated the PDs’ distribution, while it’s assumed that the indicators are distributed according to the multidimensional subordinated Lévy model (Variance Gamma model and Normal Inverse Gaussian model, particularly). Although the obtained results show that all banks are relatively healthy, there is still high chance that “a financial crisis” will occur, at least in terms of probability. This is indicated by estimation of the various quantiles in the estimated distributions. Finally, it should be noted that the applicability of the estimated model (with respect to the used data) is limited to the recessionary phase of the financial market.

**Keywords:**
Credit-scoring Models,
Multidimensional
Subordinated Lévy Model,
Probability of Default.

##### 2200 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.