Generation of Random Gamma Variates from the Two-Parameter Gamma

An algorithm has been developed capable of generating random gamma variates from any two-parameter gamma form with arbitrary parameters. The algorithm, shown to be both accurate and computationally efficient, is given as a FORTRAN IV function routine. Extensions are also made to the generation of random deviates from other useful probability density functions.     

Theoretical Foundations of Gamma–Gamma Method of Detection of Explosives

Theoretical calculations of the spectra of gamma radiation scattered by trinitrotuluene and by substances that are close to trinitrotuluene in terms of density and composition are presented. From the results of calculations, requirements that must be satisfied by a method of detection and identification of different explosives and a device to implement the method are formulated.     

Gamma Irradiation of Hexafluorobenzene

Mixtures of hexafluorobenzene and benzene were irradiated in liquid phase by means of a Co⁶⁰ gamma source at 20° and at 218° C. Perfluoroheptane and various binary mixtures involving perfluoroheptane, hexafluorobenzene, benzene, and cyclohexane were also irradiated at 20° C. Hexafluorobenzene resembled benzene very closely in its behavior upon radiolysis. Generally the fluorocarbon-hydrocarbon mixtures evolved much more SiF₄ (indicating the formation of HF, which reacts with the glass vessel) than the pure fluorocarbon components. The polymer from hexafluorobenzene-benzene mixtures was probably rich in cyclohexadiene and cyclohexene units, resembling that from pure benzene, and its composition ratio exhibited a strong “alternating” tendency. The results are discussed in terms of free-radical and excited-state mechanisms. At 218° C hexafluorobenzene and also its mixtures with benzene showed qualitative differences from their behavior at 20° C, although the G values for SiF₄ and polymer remained moderate.     

Inference on the Gamma Distribution

This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for the gamma shape parameter is derived. The generalized confidence intervals for the rate parameter and other quantities such as mean are explored. The proposed generalized inferential procedures are extended to construct prediction limits for a single future measurement and for at least p of m measurements at each of r locations. The performance of the proposed procedures is evaluated using Monte Carlo simulation. The simulation results show that the proposed procedures are very satisfactory. Finally, three real examples are used to illustrate the proposed procedures. Supplementary materials for this article are available online.     

Simulation of Arbitrary Gamma Distributions

Two simulation procedures for arbitrary gamma distributions are compared. Both procedures depend on closed form approximations to the cumulative gamma distributions, but one procedure appears to yield considerably more accurate results than the other. Tables are given which allow this procedure to be easily applied.     

Gamma Irradiation of Fluorocarbon Polymers

Several fluorocarbon polymers were irradiated with Co⁶⁰ gamma radiation at doses up to 10²² ev/g. The polymers studied included polytetrafluoroethylene, polytrifluoroethylene, polychlorotrifluoroethylene, a copolymer of tetrafluoroethylene with hexafluoropropylene, and several rubbery vinylidene fluoride copolymers. G-values were measured for volatile products, for free radicals detected by electron spin resonance, and, in the case of polychlorotrifluoroethylene, for scissions. The course of degradation or crosslinking was followed by zero-strength-time and tensile-strength measurements. It was found that for polytetrafluoroethylene and its hexafluoropropylene copolymer the presence of air-accelerated scission drastically. The mechanism of the radiation-induced changes is discussed in terms of free-radical intermediates.     

Bayesian Availability Using Gamma Distributed Priors

Classical statistical estimation techniques have limited usage in predicting system availability when a system, e.g., a computer or telecommunications system, is highly reliable. A Bayesian solution is suggested in this paper. Gamma priors, which are rich in shapes, are assigned to the scale parameters of a gamma distributed component on-time and off-time. Estimation of the gamma priors follows engineer's past experiences for reliability modeling. Both steady-state and instantaneous availabilities are derived using Bayes Theorem. An illustration highlights the assessment and evaluation of the proposed availability measure.     

Gamma Ti aluminides for non-aerospace applications

Attempts to utilize gamma Ti aluminide in non-aerospace applications have centered on components for which weight reduction would improve overall equipment performance, namely exhaust valves and turbocharger turbines for automotive engines. As a result of extensive research that has recently been conducted on materials, manufacturing processes, and application tests for those two types of components, both have reached the point of practical utilization. However, the development of low-cost manufacturing processes is still needed for expanded practical application in the future.     

主动式有机发光显示器的伽马校正(英文)

针对平板显示器在光电转换过程中出现的非线性关系,视频图像在处理过程中引入了伽马校正。本文提出了一种关于0.5英寸主动式有机发光显示器SVGA050D的伽马校正方法。该方法根据查找表的对应关系,采用PIC单片机作为主控芯片,通过串行总线通信配置显示器和解码芯片等内部寄存器生成查找表的方式,实现了输入为VGA或复合视频信号的伽马校正。经实验验证,校正功能得到了有效的实现,视频图像的质量明显改进。     

Order Statistics from the Gamma Distribution

This paper deals with order statistics from a gamma or χ² (Pearson Type III) distribution. Expressions are derived for the moments of an order statistic and for the covariance between two order statistics. A table of moments (about the origin as well as the mean) is presented. Equations are derived which are used to solve for the percentage points of the order statistics and a table of the percentage points is given. The problem of the best linear unbiased estimate of the scale parameter of the distribution which is based on order statistics is, briefly, discussed for the censored (type II) case. The modal value of an order statistic is derived and a table of these values is given for the cases of the smallest and the largest order statistics. Applications ‘to life-tests, extreme values, reliability and maintenance are described and illustrated in some cases.     

Gamma Approximation for Preventive Maintenance Scheduling

This paper presents an approximation model for determining minimum cost preventive maintenance schedules where accurate failure data are not available except the “average” (mean) and the “typical” value (mode) of the component lifetime.     

Gamma Sorbitol as a Diluent in Tablets

Abstract

Several crystal structures of Sorbitol may be encountered. Eleven Sorbitol samples from five different manufacturers were studied by X Ray diffraction and differential scanning calorimetry. Three crystalline forms were identified. The γ form is the most stable. One of these samples was constituted by the pure γ form.

Sorbitol is usually considered as a very hygroscopic excipient. We studied this most stable Sorbitol for its technological and biopharmaceutical properties in tablet formulation.

Aspirin and Acid Ascorbic tablets were prepared with γ Sorbitol as a diluent, in high concentration, by direct compression. Three disintegrants were tested: maize starch, Kollidon CL^R, Ac Di Sol^R. Using either lactose or γ Sorbitol as a diluent, different batches of tablets were prepared with the same proportion of diluent and in the same conditions.

Compression properties, hardness, disintegration time, dissolution rate and stability in moist conditions were studied.

The tablets containing γ Sorbitol show:

- a better ratio compression force/hardness

- a longer time of disintegration and dissolution

- the very great importance of the choice of the disintegrant: Ac Di Sol was much better than Kollidon CL or Maïze starch in this case of formulation: conserved during one year at 80% Relative Humidity, tablets with γ Sorbitol and Ac Di Sol kept their aspect and their biopharmaceutical properties very well. A slightly greater acid ascorbic alteration with Sorbitol as a diluent than with lactose can be noticed.

It seems that γ Sorbitol is a stable diluent if the Relative Humidity is lower than 80%. Then it should be avoided with drugs too sensitive to moisture like ascorbic acid.

In spite of a slower release time, its hardening power and its very good compression properties can be of great interest.     

Developers for High Speed with Low Gamma

77B-4 melol hydroquinone developer ensures considerable speed gain as compared to the D-76 developer (both developers with 6 gr.ll potassium bromide) due to a higher reduction potential value of the former. 17B-4 renders higher speed thon a similar developer with a pH 9-6 buffer solution especially when developing intensive short exposures. The reduction potential value besides the processing time is of paramounl importance for obtaining high speed with low gamma.     

Gamma correction for digital fringe projection profilometry

Digital fringe projection profilometry utilizes a digital video projector as a structured light source and thus gains great flexibility. However, the gamma nonlinearity of the video projector inevitably decreases the accuracy and resolution of the measurement. We propose a gamma-correction technique based on statistical analysis of the fringe images. The technique allows one to estimate the value of gamma from the normalized cumulative histogram of the fringe images. By iterating the two steps, gamma estimation and phase evaluation, the actual gamma value can be calculated. At the same time the phase distribution of the fringe pattern can be solved with higher accuracy. In so doing, neither photometric calibration nor knowledge of the device is required. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.