• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.625-639
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• 2020

The gamma distribution is a flexible right-skewed distribution widely used in many areas, and it is of great interest to estimate the probability of a random variable exceeding a specified value in survival and reliability analysis. Therefore, the study develops a fixed-accuracy confidence interval for P(X > c) when X follows a gamma distribution, Γ(α, β), and c is a preassigned positive constant through: 1) a purely sequential procedure with known shape parameter α and unknown rate parameter β; and 2) a nonparametric purely sequential procedure with both shape and rate parameters unknown. Both procedures enjoy appealing asymptotic first-order efficiency and asymptotic consistency properties. Extensive simulations validate the theoretical findings. Three real-life data examples from health studies and steel manufacturing study are discussed to illustrate the practical applicability of both procedures.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• KCID journal
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• v.5 no.1
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• pp.32-46
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• 1998

This study was conducted to derive optimal design floods by generalized gamma distribution model of the annual maximum series at six watersheds along Han and Nag Dong river systems. Design floods obtained by different methods for estimation of parameters

• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.138-144
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• 2014

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. The more the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica programs we derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory.

• Water for future
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• v.18 no.4
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• pp.317-325
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• 1985

In the analysis, monthly streamflow records atthe gauging station in Nakdong, Han and Geum river were used. Also, the fitness of monthly streamflow to Gamma and Long-normal distribution was tested by Kolomogorv-Smirnov test. The results obtained in this study can be summarized as follws (1) The fitness of monthly streamflow to two-parameter Gamma distribution was tested by Kolomorov-Smirnov test, which fits well to this Gamma distribution (2) The Run-length and Run-sum were simulated by the Gamma model. In this result, run-length and Run-sum of monthly streamflow were fit for Gamma model (3) The mean decreases (increases) the expected surplus (deficit) Run-Sum of the monthly streamflow. The higher the truncation level of negative Run-length and Run-sum the larger is the effect of mean.

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.125-130
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• 2005

Coalescence process of binary immiscible fluid mixtures having bimodal size distributions, prepared by mixing two pre-sheared samples at different shear rates, ${\gamma}_{pre1}\;and\;{\gamma}_{pre2}$, under shear flow at a final shear rate, ${\gamma}_f$, are examined by transient shear stress measurements and microscopic observations in comparison with the results for simply pre-sheared samples having narrow size distributions (unimodal distribution samples). Component fluids are a silicone oil (PDMS) and a hydrocarbon-formaldehyde resin (Genelite) and their viscosities are 14.1 and 21.0 $pa{\cdot}sec$ at room temperature $(ca.\;20^{\circ}C)$, respectively. The weight ratio of PDMS: Genelite was 7:3. Three cases, $({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;({\gamma}_{pre1}=0.8sec^{-1},\;{\gamma}_{pre2}=4.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;and\;({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0^sec^{-1}\;and\;{\gamma}_f=7.2sec^{-1})$ the first case, transient shear stress did not show any significant difference but domains larger than the initial state are observed at short times. In the latter cases, there exist undershoot of shear stress, reflecting existence of deformed large domains, which is confirmed by the direct observation. It is concluded that coalescence between large and small domains more frequently occur than coalescence between the domains with similar size in the bimodal distribution samples.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.265-279
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• 1999

In this study, one of the techniques on the extension of low flow series has been developed, in which the daily streamflows were simulated by the Tank model with the input of extended daily rainfall series which were stochastically generated by the Markov chain model. The annual lowest flow serried for each of the given durations were formulated form the simulated daily streamflow sequences. The frequency of the estimated annual lowest flow series was analyzed. The distribution types to be used for the frequency analysis were two-parameter and three-parameter log-normal distribution, two-parameter and three-parameter Gamma distribution, three-parameter log-Gamma distribution, Gumbel distribution, and Weibull distribution, of which parameters were estimated by the moment method and the maximum likelihood method. The goodness-of-fit test for probability distribution is evaluated by the Kolmogorov-Sminrov test. The fitted distribution function for each duration series is applied to frequency analysis for developing duration-low flow-frequency curves at Yongdam Dam station. It was shown that the purposed technique in this study is available to generate the daily streamflow series with fair accuracy and useful to determine the probabilistic low flow in the watersheds having the poor historic records of low flow series.

• Progress in Medical Physics
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• v.26 no.1
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• pp.42-51
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• 2015

In proton therapy, verification of proton dose distribution is important to treat cancer precisely and to enhance patients' safety. To verify proton dose distribution, in a previous study, our team incorporated a vertically-aligned one-dimensional array detection system. We measured 2D prompt-gamma distribution moving the developed detection system in the longitudinal direction and verified similarity between 2D prompt-gamma distribution and 2D proton dose distribution. In the present, we have developed two-dimension prompt-gamma measurement system consisted of a 2D parallel-hole collimator, 2D array-type NaI(Tl) scintillators, and multi-anode PMT (MA-PMT) to measure 2D prompt-gamma distribution in real time. The developed measurement system was tested with $^{22}Na$ (0.511 and 1.275 MeV) and $^{137}Cs$ (0.662 MeV) gamma sources, and the energy resolutions of 0.511, 0.662 and 1.275 MeV were $10.9%{\pm}0.23p%$, $9.8%{\pm}0.18p%$ and $6.4%{\pm}0.24p%$, respectively. Further, the energy resolution of the high gamma energy (3.416 MeV) of double escape peak from Am-Be source was $11.4%{\pm}3.6p%$. To estimate the performance of the developed measurement system, we measured 2D prompt-gamma distribution generated by PMMA phantom irradiated with 45 MeV proton beam of 0.5 nA. As a result of comparing a EBT film result, 2D prompt-gamma distribution measured for $9{\times}10^9$ protons is similar to 2D proton dose distribution. In addition, the 45 MeV estimated beam range by profile distribution of 2D prompt gamma distribution was $17.0{\pm}0.4mm$ and was intimately related with the proton beam range of 17.4 mm.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2015.10a
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• pp.1100-1102
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• 2015

In the study, stereo-based of gamma-ray sources detector for the space including the gamma-ray source to scan in a raster scan method, and obtains a visible light image and the gamma-ray image. We went to retrieve and visualize the distance to source and the direction of the 3-dimension information from Stereo gamma-ray detectors. Configuration of the detector consisted of gamma-ray detecting sensor for gamma-ray Sources, pan-tilt for the scanning of the raster for detecting sources, and CCD camera for visible-light image. Implement a stereo structure of the device to measure the spatial distribution of source, the gamma-ray Detector and CCD camera for the stereo image acquisition was as each configuration 2. The gamma-ray detector and a visible light camera to revision the distribution of detection source, After performing each of the cameras of the stereo correction and shows the distribution of the gamma-ray Sources through 중첩 visible light image and the gamma-ray image. After Rectification process of Left and right image, we were derived visualization results of the stereo image.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.10a
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• pp.944-945
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• 2016

Gamma-ray Detector for gamma-ray imaging device is composed of a shielding body for shielding gamma-rays incident from the radiation source. Distribution of the gamma ray can be represented by the distribution information on the direction in which the detecting section and the signal through the incident hole of collimator. The role of the shield is important because all signals should be treated as noise except for the signal from the incident hole.In this paper In this paper, we have produced a compact, lightweight and Collimator shield by changing the structure and physical properties with respect to the collimator and shielding of lead-based gamma-ray detectors. And we analyzed the shielding effectiveness relative to the incident gamma ray sphere measured signal value through the gamma irradiation test facility. The results confirmed that the production and Collimator shielding the imaging device Implementing more efficient to implement.