• Title/Summary/Keyword: Modified gamma distribution function

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Analysis on the Relations of Droplet Size Distribution and Optical Depth in Water Curtain (워터커튼에서 액적의 크기 분포와 광학 두께의 상관관계 분석)

  • You, Woo Jun;Ryou, Hong-Sun
    • Fire Science and Engineering
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    • v.30 no.2
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    • pp.62-67
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    • 2016
  • In this study, the optical depth is analyzed with the effects of droplet size distribution of the water curtain nozzle to attenuate the radiative heat transfer. The HELOS/VARIO equipment is used for the measurement of the droplet size distributions. The spray characteristics are quantified by the investigation of Deirmenjian's modified gamma distribution function. The distribution constant of the nozzle can be obtained as ${\alpha}=1$ and ${\gamma}=5.2$. The generalized equation of the optical depth related with the droplet size distribution is introduced. These results will be applicable to the analysis of the design condition of the water curtain nozzle.

A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation

  • Ibrahim, Mohamed;Yadav, Abhimanyu Singh;Yousof, Haitham M.;Goual, Hafida;Hamedani, G.G.
    • Communications for Statistical Applications and Methods
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    • v.26 no.5
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    • pp.473-495
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    • 2019
  • In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

Patient-Specific Quality Assurance in a Multileaf Collimator-Based CyberKnife System Using the Planar Ion Chamber Array

  • Yoon, Jeongmin;Lee, Eungman;Park, Kwangwoo;Kim, Jin Sung;Kim, Yong Bae;Lee, Ho
    • Progress in Medical Physics
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    • v.29 no.2
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    • pp.59-65
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    • 2018
  • This paper describes the clinical use of the dose verification of multileaf collimator (MLC)-based CyberKnife plans by combining the Octavius 1000SRS detector and water-equivalent RW3 slab phantom. The slab phantom consists of 14 plates, each with a thickness of 10 mm. One plate was modified to support tracking by inserting 14 custom-made fiducials on surface holes positioned at the outer region of $10{\times}10cm^2$. The fiducial-inserted plate was placed on the 1000SRS detector and three plates were additionally stacked up to build the reference depth. Below the detector, 10 plates were placed to avoid longer delivery times caused by proximity detection program alerts. The cross-calibration factor prior to phantom delivery was obtained by performing with 200 monitor units (MU) on the field size of $95{\times}92.5mm^2$. After irradiation, the measured dose distribution of the coronal plane was compared with the dose distribution calculated by the MultiPlan treatment planning system. The results were assessed by comparing the absolute dose at the center point of 1000SRS and the 3-D Gamma (${\gamma}$) index using 220 patient-specific quality assurance (QA). The discrepancy between measured and calculated doses at the center point of 1000SRS detector ranged from -3.9% to 8.2%. In the dosimetric comparison using 3-D ${\gamma}$-function (3%/3 mm criteria), the mean passing rates with ${\gamma}$-parameter ${\leq}1$ were $97.4%{\pm}2.4%$. The combination of the 1000SRS detector and RW3 slab phantom can be utilized for dosimetry validation of patient-specific QA in the CyberKnife MLC system, which made it possible to measure absolute dose distributions regardless of tracking mode.

New approach to calculate Weibull parameters and comparison of wind potential of five cities of Pakistan

  • Ahmed Ali Rajput;Muhammad Daniyal;Muhammad Mustaqeem Zahid;Hasan Nafees;Misha Shafi;Zaheer Uddin
    • Advances in Energy Research
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    • v.8 no.2
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    • pp.95-110
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    • 2022
  • Wind energy can be utilized for the generation of electricity, due to significant wind potential at different parts of the world, some countries have already been generating of electricity through wind. Pakistan is still well behind and has not yet made any appreciable effort for the same. The objective of this work was to add some new strategies to calculate Weibull parameters and assess wind energy potential. A new approach calculates Weibull parameters; we also developed an alternate formula to calculate shape parameters instead of the gamma function. We obtained k (shape parameter) and c (scale parameter) for two-parameter Weibull distribution using five statistical methods for five different cities in Pakistan. Maximum likelihood method, Modified Maximum likelihood Method, Method of Moment, Energy Pattern Method, Empirical Method, and have been to calculate and differentiate the values of (shape parameter) k and (scale parameter) c. The performance of these five methods is estimated using the Goodness-of-Fit Test, including root mean square error, mean absolute bias error, mean absolute percentage error, and chi-square error. The daily 10-minute average values of wind speed data (obtained from energydata.info) of different cities of Pakistan for the year 2016 are used to estimate the Weibull parameters. The study finds that Hyderabad city has the largest wind potential than Karachi, Quetta, Lahore, and Peshawar. Hyderabad and Karachi are two possible sites where wind turbines can produce reasonable electricity.

Absorbed Dose for the Endovascular Ho-166-DTPA Brachytherapy Using a Balloon Angio Catheter (풍선도자관의 Ho-166-DTPA 흡수선량)

  • 조철우;박찬희;윤석남;강해준;김미화;장지선;박경배
    • Progress in Medical Physics
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    • v.13 no.2
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    • pp.98-103
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    • 2002
  • The purpose of this study was to evaluate the absorbed dose to the coronary artery segment from various sized balloon angio catheters. The liquid form of Ho-166 was produced at the KAERI by (n, ${\gamma}$ ) reaction. We used GafChromic film for the estimation of the absorbed dose by beta particles. The exposed films were read using a videodensitometer. Several film exposures were made with varying irradiation times and activities. A modified micrometer was used for the measurement of the absorbed dose distribution near the balloon surface. Four balloons of coronary catheters evaluated were 30 m long and 2.5, 3.0, 3.5 and 4.0 mm in diameter. All doses are plotted in units of Gy/min/GBq/ml as a function of radial distance in mm from the surface of balloon. The absorbed dose rate was 0.86, 1.01, 1.11 and 1.24 Gy/min/GBq/ml at a balloon surface for various balloon diameter 2.5, 3.0, 3.5 and 4.0 mm respectively. Using a vacuum pump, the air in the balloon was evacuated prior to instillation of the Ho-166 source. By removing air bubbles in the balloon, the absorbed dose distribution was more uniform.

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