放射能測定における平均値の計算法

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タイトル別名
  • On the Calculation of the Average in Radioactivity Measurements.
  • ホウシャノウ ソクテイ ニ オケル ヘイキンチ ノ ケイサンホウ

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Three different methods for averaging the independent experimental results in radioactivity measurements are compared by using the computer simulation. The first method is the new one proposed by the author and is introduced according to the maximum likelihood method. The second and third methods are the ordinarily used ones, the simplest arithmetic mean and the weighted mean, respectively.<BR>A radioactive sample is assumed to be independently measured twice. The parent mean of the net counts per unit time, μ, is assumed to be identical in two measurements and the parent means of the background per unit time, λland λ2, are different each other.<BR>The counting data of the sample, xk (k=1, 2), are generated by the Poisson random number generator, whose parent means are of (μ+λk) tk, respectively, where tk are the accumulation periods of the sample measurements. The background data are also generated with the parent means, λkτk (k=1, 2), where τk are the accumulation periods of the background.<BR>The generated data are analysed by the different three methods. In the new method a likelihood function is firstly introduced under the above-mentioned conditions. One can then get non-linear simultaneous equations by differentiating the likelihood function with respect to μ, λland λ2. The simultaneous equations can be solved by a successive approximation, and then the estimate of μ can be obtained.<BR>The simplest arithmetic mean is carried out for the sample counts per unit time subtracted by the backgrounds per unit time. The weighted mean is done in the same manner as the case of the Gaussian-distributed data.<BR>These processes are repeated 10 000 or 20 000 times and the arithmetic means of three estimates are independently calculated according to the methods.<BR>The new method and the simplest arithmetic mean denote the similar results, each other, and both give the good estimates of the parent mean, μ. On the other hands, the weighted mean gives not good estimates, on the whole.<BR>The new method should be the most desirable for the analysis, if all of the original data in the measurements would be known. When such data cannot be known, the simplest arithmetic mean should be used in the analysis.<BR>The weighted mean is not suitable and should not be used to the analysis of the radioactivity data, in spite of its usefulness for the Gaussian-distributed data.

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