**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2312

# Search results for: generalized gamma distribution

##### 2312 On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

**Authors:**
Teerayut Chomchuen,
Aiyared Iampan

**Abstract:**

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

**Keywords:**
Γ-semiring,
bi-Γ-ideal,
generalized bi-Γ-ideal.

##### 2311 Impact of Weather Conditions on Generalized Frequency Division Multiplexing over Gamma Gamma Channel

**Authors:**
Muhammad Sameer Ahmed,
Piotr Remlein,
Tansal Gucluoglu

**Abstract:**

The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

**Keywords:**
Free space optics,
generalized frequency division
multiplexing,
weather conditions,
gamma gamma distribution.

##### 2310 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.

##### 2309 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.

##### 2308 Statistical Description of Wave Interactions in 1D Defect Turbulence

**Authors:**
Yusuke Uchiyama,
Hidetoshi Konno

**Abstract:**

**Keywords:**
sub-Poisson statistics,
hyper gamma distribution,
fractional Poisson configuration.

##### 2307 Profile Calculation in Water Phantom of Symmetric and Asymmetric Photon Beam

**Authors:**
N. Chegeni,
M. J. Tahmasebi Birgani

**Abstract:**

Nowadays, in most radiotherapy departments, the commercial treatment planning systems (TPS) used to calculate dose distributions needs to be verified; therefore, quick, easy-to-use and low cost dose distribution algorithms are desirable to test and verify the performance of the TPS. In this paper, we put forth an analytical method to calculate the phantom scatter contribution and depth dose on the central axis based on the equivalent square concept. Then, this method was generalized to calculate the profiles at any depth and for several field shapes regular or irregular fields under symmetry and asymmetry photon beam conditions. Varian 2100 C/D and Siemens Primus Plus Linacs with 6 and 18 MV photon beam were used for irradiations. Percentage depth doses (PDDs) were measured for a large number of square fields for both energies, and for 45^{º} wedges which were employed to obtain the profiles in any depth. To assess the accuracy of the calculated profiles, several profile measurements were carried out for some treatment fields. The calculated and measured profiles were compared by gamma-index calculation. All γ–index calculations were based on a 3% dose criterion and a 3 mm dose-to-agreement (DTA) acceptance criterion. The γ values were less than 1 at most points. However, the maximum γ observed was about 1.10 in the penumbra region in most fields and in the central area for the asymmetric fields. This analytical approach provides a generally quick and fairly accurate algorithm to calculate dose distribution for some treatment fields in conventional radiotherapy.

**Keywords:**
Dose distribution,
equivalent field,
asymmetric field,
irregular field.

##### 2306 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.

##### 2305 Generalized Module Homomorphisms of Triangular Matrix Rings of Order Three

**Authors:**
Jianmin Xing

**Abstract:**

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = T M D 0 U N 0 0 V .

**Keywords:**
Generalized module homomorphism,
ring homomorphism,
isomorphisms,
triangular matrix rings.

##### 2304 Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II

**Authors:**
Ahmet Tekcan,
Arzu Özkoç

**Abstract:**

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indeﬁnite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the ﬁrst section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some speciﬁc values of Q and P.

**Keywords:**
Quadratic irrationals,
quadratic ideals,
indefinite quadratic forms,
extended modular group.

##### 2303 A Generalized Coordination Setting Method for Distribution Systems with Closed-loop

**Authors:**
Kang-Le Guan,
Seung-Jae Lee,
Myeon-Song Choi

**Abstract:**

The protection issues in distribution systems with open and closed-loop are studied, and a generalized protection setting scheme based on the traditional over current protection theories is proposed to meet the new requirements. The setting method is expected to be easier realized using computer program, so that the on-line adaptive setting for coordination in distribution system can be implemented. An automatic setting program is created and several cases are taken into practice. The setting results are verified by the coordination curves of the protective devices which are plotted using MATLAB.

**Keywords:**
protection setting,
on-line system analysis,
over current protection,
closed-loop distribution system

##### 2302 On Fourier Type Integral Transform for a Class of Generalized Quotients

**Authors:**
A. S. Issa,
S. K. Q. AL-Omari

**Abstract:**

**Keywords:**
Fourier type integral,
Fourier integral,
generalized
quotient,
Boehmian,
distribution.

##### 2301 Performance Analysis of a Hybrid DF-AF Hybrid RF/FSO System under Gamma Gamma Atmospheric Turbulence Channel Using MPPM Modulation

**Authors:**
Hechmi Saidi,
Noureddine Hamdi

**Abstract:**

**Keywords:**
FSO,
RF,
hybrid,
AF,
DF,
SER,
SNR,
GG channel.

##### 2300 Compton Scattering of Annihilation Photons as a Short Range Quantum Key Distribution Mechanism

**Authors:**
Roman Novak,
Matjaz Vencelj

**Abstract:**

**Keywords:**
Compton scattering,
gamma-ray polarization,
quantumcryptography,
quantum key distribution

##### 2299 Performance Analysis of M-Ary Pulse Position Modulation in Multihop Multiple Input Multiple Output-Free Space Optical System over Uncorrelated Gamma-Gamma Atmospheric Turbulence Channels

**Authors:**
Hechmi Saidi,
Noureddine Hamdi

**Abstract:**

**Keywords:**
FSO,
MIMO,
MIMO,
multihop,
DF,
SER,
GG
channel.

##### 2298 Classification of Extreme Ground-Level Ozone Based on Generalized Extreme Value Model for Air Monitoring Station

**Authors:**
Siti Aisyah Zakaria,
Nor Azrita Mohd Amin,
Noor Fadhilah Ahmad Radi,
Nasrul Hamidin

**Abstract:**

Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.

**Keywords:**
Extreme value theory,
generalized extreme value distribution,
ground-level ozone,
return level.

##### 2297 Extreme Temperature Forecast in Mbonge, Cameroon through Return Level Analysis of the Generalized Extreme Value (GEV) Distribution

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

**Abstract:**

**Keywords:**
Return level,
Generalized extreme value (GEV),
Meteorology,
Forecasting.

##### 2296 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

**Authors:**
Yuli Hu,
Shaoquan Sun

**Abstract:**

**Keywords:**
BCI-algebras with operators,
generalized fuzzy subalgebras,
generalized fuzzy ideals,
generalized fuzzy quotient algebras.

##### 2295 Gamma Irradiation Effects on the Magnetic Properties of Hard Ferrites

**Authors:**
F. Abbas Pour Khotbehsara,
B. Salehpour,
A. Kianvash

**Abstract:**

**Keywords:**
Gamma ray irradiation,
Hard Ferrite,
Magnetic
coefficient,
Radiation dose.

##### 2294 Modelling Extreme Temperature in Malaysia Using Generalized Extreme Value Distribution

**Authors:**
Husna Hasan,
Norfatin Salam,
Mohd Bakri Adam

**Abstract:**

**Keywords:**
Extreme temperature,
extreme value,
return level.

##### 2293 Gamma Irradiation Effect on Structural and Optical Properties of Bismuth-Boro-Tellurite Glasses

**Authors:**
A. Azuraida,
M. K. Halimah,
C. A. C. Azurahanim,
M. Ishak

**Abstract:**

**Keywords:**
Boro-Tellurite,
bismuth,
gamma radiation,
optical
properties.

##### 2292 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 2291 Radiation Dose Distribution for Workers in South Korean Nuclear Power Plants

**Authors:**
B. I. Lee,
S. I. Kim,
D. H. Suh,
J. I. Kim,
Y. K. Lim

**Abstract:**

A total of 33,680 nuclear power plants (NPPs) workers were monitored and recorded from 1990 to 2007. According to the record, the average individual radiation dose has been decreasing continually from it 3.20 mSv/man in 1990 to 1.12 mSv/man at the end of 2007. After the International Commission on Radiological Protection (ICRP) 60 recommendation was generalized in South Korea, no nuclear power plant workers received above 20 mSv radiation, and the numbers of relatively highly exposed workers have been decreasing continuously. The age distribution of radiation workers in nuclear power plants was composed of mainly 20-30- year-olds (83%) for 1990 ~ 1994 and 30-40-year-olds (75%) for 2003 ~ 2007. The difference in individual average dose by age was not significant. Most (77%) of NPP radiation exposures from 1990 to 2007 occurred mostly during the refueling period. With regard to exposure type, the majority of exposures were external exposures, representing 95% of the total exposures, while internal exposures represented only 5%. External effective dose was affected mainly by gamma radiation exposure, with an insignificant amount of neutron exposure. As for internal effective dose, tritium (3H) in the pressurized heavy water reactor (PHWR) was the biggest cause of exposure.

**Keywords:**
Dose distribution,
External exposure,
Nuclear powerplant,
Occupational radiation dose

##### 2290 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

**Authors:**
Chao Yuan,
Bao Guang Tian

**Abstract:**

**Keywords:**
Generalized linear model,
generalized relative coefficient,
least eigenvalue,
relative efficiency.

##### 2289 On Q-Fuzzy Ideals in Γ-Semigroups

**Authors:**
Samit Kumar Majumder

**Abstract:**

In this paper the concept of Q-fuzziﬁcation of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semigroups.

**Keywords:**
Q-Fuzzy set,
Γ-semigroup,
Regular Γ-semigroup,
Q-Fuzzy left(right) ideal,
Operator semigroups.

##### 2288 Generalized Chebyshev Collocation Method

**Authors:**
Junghan Kim,
Wonkyu Chung,
Sunyoung Bu,
Philsu Kim

**Abstract:**

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

**Keywords:**
Generalized Chebyshev Collocation method,
Generalized Chebyshev Polynomial,
Initial value problem.

##### 2287 A CUSUM Control Chart to Monitor Wafer Quality

**Authors:**
Sheng-Shu Cheng,
Fong-Jung Yu

**Abstract:**

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.

**Keywords:**
Nonconformities,
Compound Poisson distribution,
CUSUM control chart.

##### 2286 A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data

**Authors:**
Ülkü Erişoğlu,
Murat Erişoğlu,
Hamza Erol

**Abstract:**

**Keywords:**
Exponential-Gamma,
Exponential-Weibull,
Gamma-Weibull,
EM Algorithm,
Survival Analysis.

##### 2285 (T1, T2)*- Semi Star Generalized Locally Closed Sets

**Authors:**
M. Sundararaman,
K. Chandrasekhara Rao

**Abstract:**

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

**Keywords:**
(T1,
T2)*-semi star generalized locally closed sets,
T1T2-semi star generalized closed sets.

##### 2284 Application of Gamma Frailty Model in Survival of Liver Cirrhosis Patients

**Authors:**
Elnaz Saeedi,
Jamileh Abolaghasemi,
Mohsen Nasiri Tousi,
Saeedeh Khosravi

**Abstract:**

Goals and Objectives: A typical analysis of survival data involves the modeling of time-to-event data, such as the time till death. A frailty model is a random effect model for time-to-event data, where the random effect has a multiplicative influence on the baseline hazard function. This article aims to investigate the use of gamma frailty model with concomitant variable in order to individualize the prognostic factors that influence the liver cirrhosis patients’ survival times. Methods: During the one-year study period (May 2008-May 2009), data have been used from the recorded information of patients with liver cirrhosis who were scheduled for liver transplantation and were followed up for at least seven years in Imam Khomeini Hospital in Iran. In order to determine the effective factors for cirrhotic patients’ survival in the presence of latent variables, the gamma frailty distribution has been applied. In this article, it was considering the parametric model, such as Exponential and Weibull distributions for survival time. Data analysis is performed using R software, and the error level of 0.05 was considered for all tests. Results: 305 patients with liver cirrhosis including 180 (59%) men and 125 (41%) women were studied. The age average of patients was 39.8 years. At the end of the study, 82 (26%) patients died, among them 48 (58%) were men and 34 (42%) women. The main cause of liver cirrhosis was found hepatitis 'B' with 23%, followed by cryptogenic with 22.6% were identified as the second factor. Generally, 7-year’s survival was 28.44 months, for dead patients and for censoring was 19.33 and 31.79 months, respectively. Using multi-parametric survival models of progressive and regressive, Exponential and Weibull models with regard to the gamma frailty distribution were fitted to the cirrhosis data. In both models, factors including, age, bilirubin serum, albumin serum, and encephalopathy had a significant effect on survival time of cirrhotic patients. Conclusion: To investigate the effective factors for the time of patients’ death with liver cirrhosis in the presence of latent variables, gamma frailty model with parametric distributions seems desirable.

**Keywords:**
Frailty model,
latent variables,
liver cirrhosis,
parametric distribution.

##### 2283 Effects of Gamma Irradiation on Chemical and Antioxidant Properties of Iranian Native Fresh Barberry Fruit

**Authors:**
Samira Berenji Ardestani,
Hamid Reza Akhavan

**Abstract:**

*Berberis vulgaris*) during refrigerated storage for 40 days were evaluated. The total anthocyanin and total phenolic contents of barberry fruits decreased in a dose-dependent manner immediately after irradiation and after subsequent storage. In general, it is recommended that, according to the effect of gamma radiation on physicochemical, microbial and sensorial characteristics, doses of 1.25-2 kGy could be used.

**Keywords:**
Antioxidant property,
barberry fruit,
chemical properties,
gamma irradiation.