• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.133-142
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• 1998

This paper is a brief review of the different procedures that are available for fitting theoretical distributions to data. The use of each technique is illustrated by reference to a distribution system which including the Pearson, Poission approximation of Gamma distribution and Burr functions. These functions can be used to calculate percent out of specification. Therefore, in this paper a new methods for estimating a measure of non-normal process capability for Gamma distributed variable data proposed using the percentage nonconforming. Process capability indices combines with the percentage nonconforming information can be used to evaluate more accurately process capability.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.

• Journal of radiological science and technology
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• v.24 no.1
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• pp.49-53
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• 2001

A number of radionuclides of interest in nuclear medicine are short lived isotopes that emit only gamma ray. The most of all Dept. of Nuclear Medicine in the hospt. are using the $^{99}Mo-^{99m}Tc$ generator for elution of the short lived isotope $^{99m}TcO_4$. A $^{99}Mo-^{99m}Tc$ generator consists of an alumina column on which $^{99}Mo$ is bound. The parent isotope($^{99}Mo$ : half life 67 hr.) decays to its daughter $^{99m}TcO_4^-$ which is a different element with a shorter half-life. $^{99}Mo$ emitted 41-keV(1.3%), 141-keV(5.6%) 181-keV(6.6%) and 366-keV(1.5%) gamma rays. But $^{99m}TcO_4$ emitted only 140-keV gamma ray. We study about the gamma ray distribution around the $^{99}Mo$ generator. And obtained the result as follows ; 1. Total counted gamma ray from generator smaller in front side than back. 2. The gamma ray emitted from $^{99}Mo$ generator without $^{99m}TcO_4$ vial increased in the back side(Mo column posited side) 3. The gamma ray only from the $^{99m}TcO_4$ vial increased in the front side. 4. Apron can protect gamma ray above 60% of total radiation from the $^{99}Mo$ generator.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.103-111
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• 1996

This paper provides a test of the composite hypothesis that a random sample is (two parameter) gamma distributed when both the scale and shape parameters are estimated from the data. The test statistic is a variant of the usual Anderson-Darling statistic, the primary difference being that the statistic is based on the maximum likelihood estimator of the shape parameter of the assumed gamma distribution. The percentage points are developed via simulation and are presented graphically. Examples are provided.

• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.55-60
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• 1987

A rectifying inspection plan which assumes a gamma - prior distribution on the lot percent defective is considered. This sampling inspection plan is developed for finite lot sizes with matching OC curves and generated from an initial plan selected from KS A 3102 single sampling by attributes. Comparisons are made with each plan by three examples.

• Journal of Korean Medicine for Obesity Research
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• v.4 no.1
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• pp.1-11
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• 2004

Objectives: The effects of peroxisome proliferator-activated receptor ${\gamma}2\;(PPAR{\gamma}2)$ Pro12Ala (P12A) polymorphism on body mass index (BMI) and type 2 diabetes are well documented; however, until now, only a few studies have evaluated the effects of this polymorphism on body fat distribution. This study was conducted to elucidate the effects of this polymorphism on computed tomography (CT)-measured body fat distribution and other obesity-related parameters in Korean female subjects. Methods & Results: The frequencies of $PPAR{\gamma}2$ genotypes were: PP type, 93.0%; PA type, 6.8%; and AA type, 0.2%. The frequency of the A allele was 0.035. Body weight (P .012), BMI (P .012), and waist-to-hip ratio (WHR) (P .001) were significantly higher in subjects with PA/AA compared with subjects with PP. When body composition was analyzed by bioimpedance analysis, lean body mass and body water content were similar between the 2 groups. However, body fat mass (P .003) and body fat percent (P .025) were significantly higher in subjects with PA/AA compared with subjects with PP. Among overweight subjects with BMI of greater than 25, PA/AA was associated with significantly higher abdominal subcutaneous fat (P .000), abdominal visceral fat (P .031), and subcutaneous upper and lower thigh adipose tissue (P .010 and .013). However, among lean subjects with BMI of less than 25, no significant differences associated with $PPAR{\gamma}2$ genotype were found, suggesting that the fat-accumulating effects of the PA/AA genotype were evident only among overweight subjects, but not among lean subjects. When serum lipid profiles, glucose, and liver function indicators were compared among overweight subjects, no significant difference associated with $PPAR{\gamma}2$ genotype was found. Changes in body weight, BMI, WHR, and body fat mass were measured among overweight subjects who finished a 1-month weight lose program of a hypocaloric diet and exercise; no significant differences associated with $PPAR{\gamma}2$ genotype were found. Conclusions: The results of this study suggest that the $PPAR{\gamma}2$ PA/AA genotype is associated with increased subcutaneous and visceral fat areas in overweight Korean female subjects, but does not significantly affect serum biochemical parameters and outcomes of weight loss programs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.223-230
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• 2012

The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.245-261
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• 2018

Attempts have been made to define new classes of distributions that provide more flexibility for modelling skewed data in practice. In this work we define a new extension of the generalized gamma distribution (Stacy, The Annals of Mathematical Statistics, 33, 1187-1192, 1962) for Marshall-Olkin generalized gamma (MOGG) distribution, based on the generator pioneered by Marshall and Olkin (Biometrika, 84, 641-652, 1997). This new lifetime model is very flexible including twenty one special models. The main advantage of the new family relies on the fact that practitioners will have a quite flexible distribution to fit real data from several fields, such as engineering, hydrology and survival analysis. Further, we also define a MOGG mixture model, a modification of the MOGG distribution for analyzing lifetime data in presence of cure fraction. This proposed model can be seen as a model of competing causes, where the parameter associated with the Marshall-Olkin distribution controls the activation mechanism of the latent risks (Cooner et al., Statistical Methods in Medical Research, 15, 307-324, 2006). The asymptotic properties of the maximum likelihood estimation approach of the parameters of the model are evaluated by means of simulation studies. The proposed distribution is fitted to two real data sets, one arising from measuring the strength of fibers and the other on melanoma data.