The relation between the binominal and trinominal model : a critical note on the paper Rubinstein(2000)

Rubinstein(2000）論文のパラメータ設定を検討のところ，リターン期待値，分散の値に整合性がみられない。本稿は2項モデルと3項モデルとの関係に関し， Rubinstein(2000）の枠組みではどのような条件設定が考えられるかを検討し，リターン期待値，分散の値に整合性の観点からはJarrow& Rudd(1983）のモデルの方が適切であることを考察する

サン ヨウイン ユウドヒ ケンテイ ト x^2 ケンテイ オ ヨビ ソノ ザンサ ブンセキホウ

3要因クロス表の尤度比検定(x^2検定)には, 18個のモデルがあるが, 実質的には8個のモデルに包含される, その8個のモデルうち7個のモデルでは直接期待値を算出できる.残りの1種類は, 繰り返し法によって期待値を推定する必要がある(篠原 1989).これらの8個のモデルのうち3個は期待値を周辺度数を固定して算出モデルである.本研究では, これらのモデルのほかに, 期待度数に均等分布を仮定した4つのモデルのほかに, 期待度数に均等分布を仮定した4つのモデルを, 具体的な計算方法とともに残差分析法も含めて説明した

Kernel Matrix Completion

学位記番号：理工博甲2

乱数生成による誤差評価の教材の開発

I developed the teaching materials for the purpose of a student learning such as the meaning of confidence interval, and the difference between standard deviation of a sample and the standard error of the mean, and so on, by analyzing numerical data by his own hand. By performing data analysis by the Excel, it is shown that a set of pseudo random numbers (the sample-1, n = 106) generated by the programming source code ①, which is written in "Decimal BASIC", could be regarded as equal to a sample which is sampling from the population with the standard normal distribution. Therefore it turns out to be possible to treat the random numbers generated by the source code ① as hypothetical measurements including errors obeying the axioms of error. At first, a set of random numbers (sample-3, n=500) is generated by the source code ①, and then, copied onto the Excel sheet, in the teaching materials. A learner makes scatter diagrams, box-and-whisker plots, and histograms based on these data, and visually recognizes the distribution of the random numbers. Fitting Gaussian line to the histogram will aid in geometrical understanding of the meaning of the statistics such as mean and the standard deviation of the sample. Finally, 30 samples of n = 25 are generated, and analyzed. Comparing the basic statistic of each samples shows that there is possibility of the true value (the mean of the population) being not included in the range of 95 % confidence interval of the mean of the samples