Mathematica 8.0 引入全新的計算方式就是關於自由格式輸入法，只要輸入日常英語且無需語法，就能獲得想要的結果。其運作流程的關鍵點包含了世上最高級的統計運算能力與最先進的圖像處理技術。因此本文主要探討關於機率統計方面的動態操作應用。大致內容可分為動態模組、敘述統計量與資料視覺化、機率分佈和假設檢定。此外，藉由擷取軟體內建系統或教科書上的數據資料
運用在範例作介紹。

Mathematica 8 introduces a free-form language input as the new method of calculation. Enter everyday English - no syntax, you can get results. It is a new entry point of the mma workflow, including the world's most advanced statistical computing power and the most advanced image processing. In this paper, we investigate the applications of Mathematica 8.0 in probability and statistics including dynamic module, descriptive statistics and data visualization,
probability distribution and hypothesis testing. Moreover, we
provide related examples by retrieving the data of built-in system
or textbooks.

致謝....................................................................................................................i
摘要....................................................................................................................ii
Abstract............................................................................................................... iii
表次....................................................................................................................viii
圖次....................................................................................................................xi
第一章 前言
第二章 動態模式應用
2.1 Manipulate 指令.....................................................................................................5
2.1.1 指令的用法: Manipulate............................................................................................5
2.1.2 動態播放控制: Trigger、Animator、Manipulator .....................................................................7
2.1.3 點選項目控制: CheckboxBar、TogglerBar、SetterBar、RadioButtonBar、PopupMenu.......................................9
2.1.4 滾動拉軸控制: Slider、Vertical、Slider、Slider2D..................................................................11
2.1.5 其他操控方面: InputField、Locator.................................................................................13
2.2 獨立型指令..........................................................................................................14
2.2.1 動態控制: Animate.................................................................................................14
2.2.2 選單、點選控制: MenuView、TabView.................................................................................16
2.2.3 開啟項目控制: OpenerView..........................................................................................19
2.2.4 ¬翻動控制: FlipView...............................................................................................19
2.3 動態型指令..........................................................................................................21
2.3.1 動態指令: Dynamic.................................................................................................21
2.3.2 動態模組: DynamicModule...........................................................................................22
2.3.3 動態控制物件: Opener、Button、ActionMenu..........................................................................24
第三章 敘述統計量與資料視覺化
3.1 敘述統計量.........................................................................................................30
3.1.1 位置統計量: Mean、GeometricMean、HarmonicMean、TrimmedMean、RootMeanSquare、Commonest、Median.....................30
3.1.2 分散性統計量: Variance、StandardDeviation、MeanDeviation、MedianDeviation、InterquartileRange、QuartileDeviation..32
3.1.3 形狀統計量:CentralMoment、Skewness、Kurtosis、QuartileSkewness ...................................................35
3.2 統計圖表............................................................................................................36
3.2.1 資料繪圖:ListPlot、ListLinePlot、ListLogPlot、ListLogLinearPlot、ListLogLogPlot、ErrorListPlot、DateListPlot、
PairwiseScatterPlot.....................................................................................................37
3.2.2 統計圖型類別: BarChart、Histogram、ParetoPlot、PieChart、BoxWhiskerChart..........................................42
3.2.3 分布數據配適: QuantilePlot、ProbabilityPlot、ProbabilityScalePlot.................................................50
3.3 數據資料庫..........................................................................................................53
3.3.1 財金資料: FinancialData...........................................................................................54
3.3.2 國家資料: CountryData.............................................................................................56
3.3.3 城市資料: CityData................................................................................................58
3.3.4 氣候資料: WeatherData.............................................................................................59
3.3.5 色調資料: ColorData...............................................................................................61
3.4 範例................................................................................................................63
第四章 機率分布函數
4.1 隨機變數............................................................................................................74
4.1.1 機率函數指令: PDF、CDF............................................................................................76
4.1.2 一班應用指令: Mean、Variance、StandardDeviation、Skewness、Kurtosis、MomentGeneratingFunction.....................78
4.2 離散型機率分佈......................................................................................................81
4.2.1 超幾何分布: HypergeometricDistribution............................................................................82
4.2.2 常見單變量離散型機率分佈: BernoulliDistribution、BinomialDistribution、DiscreteUniformDistribution、
GeometricDistribution、NegativeBinomialDistribution、PoissonDistribution ...............................................85
4.2.3 多變量離散型分佈: MultinomialDistribution、NegativeMultinomialDistribution、MultivariatePoissonDistribution、
Covariance、Correlation、MultivariateSkewness、MultivariateKurtosis ....................................................90
4.3 連續型機率分佈......................................................................................................92
4.3.1 常態分佈: NormalDistribution . . . . . . . . . . . . . . . . …………. .....92
4.3.2 常見單變量連續型機率分佈: BetaDistribution、CauchyDistribution、ChiSquareDistribution、ExponentialDistribution、
FRatioDistribution、....................................................................................................95
4.3.3 多變量連續型分佈: BinormalDistribution、MultinormalDistribution、MultivariateTDistribution、
HotellingTSquareDistribution............................................................................................101
4.4 分佈相關應用 .......................................................................................................104
4.4.1 條件機率與期望值: Probability、Expectation........................................................................105
4.4.2 邊際分佈、分佈轉換與順序統計量: MarginalDistribution、TransformedDistribution、OrderDistribution..................107
4.4.3 混和、參數混和分佈與配適分佈參數: MixtureDistribution、ParameterMixtureDistribution、FindDistributionParameters...109
4.4.4 截斷和結尾分佈: TruncatedDistribution、CensoredDistribution.......................................................112
4.4.5 多為分佈相關應用: CopulaDistribution、ProductDistribution.........................................................114
4.4.6 無母數機率分佈: HistogramDistribution、SmoothKernelDistribution、EmpiricalDistribution、SurvivalDistribution......117
4.5 收斂的概念..........................................................................................................120
4.5.1 大數法則..........................................................................................................120
4.5.2 中央極限定理......................................................................................................122
4.5.3 漸進分佈..........................................................................................................123
4.6 範例................................................................................................................127
第五章 統計推論
5.1 常見假設檢定與信賴區間..............................................................................................144
5.1.1 單一樣本平均值....................................................................................................144
5.1.2 雙樣本平均值......................................................................................................150
5.1.3 單一樣本變異數....................................................................................................158
5.1.4 雙樣本變異數......................................................................................................161
5.1.5 單一樣本比例......................................................................................................165
5.1.6 雙樣本比例........................................................................................................167
5.2 一般假設檢定........................................................................................................169
5.2.1 位置檢定: LocationTest、LocationEquivalenceTest...................................................................170
5.2.2 分佈配適檢定: DistributionFitTest.................................................................................175
5.2.3 變異數分析: ANOVA.................................................................................................180
參考文獻
A Mathematica 8.0 機率統計..............................................................................................189
A.1 動態模式運用........................................................................................................189
A.2 統計資料視覺化......................................................................................................191
A.3 機率分佈函數........................................................................................................194
A.4 統計推論............................................................................................................198
B 引用資料..............................................................................................................200
索引....................................................................................................................213

Klein, J. P. and Moeschberge, M. L. (1997). Survival Analysis Techniques for Censored and Truncated Data. New York: Springer.

Lind, D. A. (2008). Basic Statistics for Business and Economics 6th edition. New York: McGraw-Hill Higher Education.

Montgomery, D. C. (2009a). Design and Analysis of Experiments, 7th edition. New York: John Wiley & Sons, Inc.

Montgomery, D. C. (2009b). Statistical Quality Control a Modern Introduction, 6th edition. New York: John Wiley & Sons, Inc.

Montgomery, D. C., Peck, E. A. and Vining, G. G. (2009). Introduction to Linear Regression Analysis. 4th edition. New York: John Wiley & Sons, Inc.

Rencher, A. C. (2002). Methods of Multivariate Analysis, 2nd edition. New York: John Wiley & Sons, Inc.

Ruskeep”a”a H. (2009). Mathematica Navigator: Mathematics, Statistics, and Graphics, 3rd edition. New York: Academic Press.

The R Project for Statistical Computing (2012). R Sources. http://www.r-project.org
Wolfram Research (2012). Mathematica 8.0 文件中心。
http://reference.wolfram.com/mathematica/guide/Mathematica.html
動態視覺化：
http://reference.wolfram.com/mathematica/guide/DynamicVisualization.html
統計圖形應用：
http://reference.wolfram.com/mathematica/guide/StatisticalVisualization.html
數據資料庫：
http://reference.wolfram.com/mathematica/tutorial/ComputableDataOverview.html
基礎統計量：
http://reference.wolfram.com/mathematica/tutorial/BasicStatistics.html
敘述統計量：
http://reference.wolfram.com/mathematica/guide/DescriptiveStatistics.html
離散型機率分佈：
http://reference.wolfram.com/mathematica/tutorial/DiscreteDistributions.html
連續型機率分佈：
http://reference.wolfram.com/mathematica/tutorial/ContinuousDistributions.html
機率分佈相關應用：
http://reference.wolfram.com/mathematica/ref/MarginalDistribution.html
http://reference.wolfram.com/mathematica/ref/StatisticalDistributionFunctions.html
自定與轉換機率分佈：
http://reference.wolfram.com/mathematica/ref/ProbabilityDistribution.html
http://reference.wolfram.com/mathematica/guide/DerivedDistributions.html
無母數機率分佈：
http://reference.wolfram.com/mathematica/guide/NonparametricStatisticalDistributions.html
信賴區間與 P 值：
http://reference.wolfram.com/mathematica/HypothesisTesting/tutorial/HypothesisTesting.html
假設檢定：
http://reference.wolfram.com/mathematica/guide/HypothesisTests.html
曲線配適：
http://reference.wolfram.com/mathematica/tutorial/CurveFitting.html
機率分佈配適：
http://reference.wolfram.com/mathematica/ref/EstimatedDistribution.html
http://reference.wolfram.com/mathematica/ref/FindDistributionParameters.html

林宗嶽 (2011)。Mathematica 軟體在機率與統計上的應用。 台灣高雄市國立中山大學碩士論文。

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