本論文是介紹 Mathematica 數學軟體在 7 版與 8 版中的機率統計應用，所涵蓋的範圍主要有統計資料與圖表，基礎統計應用，機率分佈，假設檢定，分佈配適，迴歸分析和集群分析等主題。當中除了介紹各種相關的指令，還有實作對應範例，
可以作為機率統計領域上對於本軟體有興趣人士參考的工具書。

In this paper, I'll introduce the applications of Mathematica 7th and 8th edition in probability and statistics. The major contents are statistical data and charts, basis statistics, probability distributions, hypothesis testing, distribution fitting, regression analysis, cluster analysis and so on. Except introducing variously related commands, this paper will provides corresponding examples, so it can be regarded as a toolbook for people interested in the probabilities and statistical parts of this software.

致謝 ......................................... i
摘要 ......................................... ii
Abstract ....................................... iii

表次 vii

第一章 前言 1

第二章 統計資料與圖表 3
2.1資料陣列整理 ................................ 3
2.1.1陣列介紹 .............................. 3
2.1.2規則陣列 .............................. 5
2.1.3部分陣列與元素的資訊 ....................... 6
2.1.4陣列修改與應用 .......................... 7
2.2資料數據與表格 .............................. 10
2.2.1 Mathematica 資料 ......................... 10
2.2.2資料操作 .............................. 18
2.3統計圖形應用 ................................ 22
2.3.1一般分佈作圖 ........................... 22
2.3.2分組分佈作圖 ........................... 28
2.3.3分佈配適作圖 ........................... 32

第三章 統計基礎應用 38
3.1數據模擬 .................................. 38
3.2基礎統計量 ................................. 40
3.3敘述統計量 ................................. 45
3.3.1位置型統計量 ........................... 45
3.3.2分散型統計量 ........................... 46
3.3.3形狀型統計量 ........................... 47
3.3.4動差方法與期望值 ......................... 48

第四章 機率分佈 56
4.1離散型機率分佈 .............................. 56
4.2連續型機率分佈 .............................. 60
4.3機率分佈相關應用 ............................. 65
4.3.1 一般應用指令............................. 65
4.3.2 機率與期望值應用指令.............................67
4.3.3 動差生成函數應用指令............................. 70
4.4 自定與轉換機率分佈.............................74
4.5 無母數機率分佈.............................80

第五章 信賴區間與假設檢定 86
5.1信賴區間與 P 值 .............................. 86
5.1.1給定數據的信賴區間指令 ...................... 87
5.1.2給定參數的信賴區間指令 ...................... 88
5.1.3 P 值指令 .............................. 89
5.2假設檢定 .................................. 92
5.2.1位置型檢定指令 .......................... 92
5.2.2變異數檢定指令 .......................... 97
5.2.3無母數適合度檢定指令 .......................... 100

第六章 基礎分佈配適 114
6.1曲線配適 ... . . . . . . . ... . . . . . . . ... . . . . . . . ... . 114
6.1.1線性配適 . . . . . . . ... . . . . . . . ... . . . . . . . ... 114
6.1.2非線性配適 . . . . . . ... . . . . . . . ... . . . . . . . ... 115
6.2機率分佈配適 .. . . . . . . . ... . . . . . . . ... . . . . . . . ... 122

第七章迴歸模型分析127
7.1 線性迴歸模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.2 廣義線性迴歸模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3 非線性迴歸模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.4 變異數分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
第八章集群分析169
8.1 資料集群分區. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2 相似元素. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

參考文獻 183

A Mathematica 統計機率指令 188
A.1統計資料與圖表 . . . . . . . ... . . . . . . . ... . . . . . . . ... 188
A.2統計基礎應用 .. . . . . . . . ... . . . . . . . ... . . . . . . . ... 190
A.3機率分佈 ... . . . . . . . ... . . . . . . . ... . . . . . . . ... . 191
A.4信賴區間與假設檢定 . . . . . ... . . . . . . . ... . . . . . . . ... 194
A.5基礎分佈配適 .. . . . . . . . ... . . . . . . . ... . . . . . . . ... 195
A.6迴歸分析 ... . . . . . . . ... . . . . . . . ... . . . . . . . ... . 195
A.7集群分析 ... . . . . . . . ... . . . . . . . ... . . . . . . . ... . 196

B 引用資料表格 198

索引 215

Anderson, D. R., Sweeney, D. J. and Williams, T. A. (2002). Statistics for Business and Economics. New York: South-Western.

DASL Project (1996). The Data and Story Library.
http://lib.stat.cmu.edu/DASL

"Auto Pollution Filter Noise." From Lewin, A. Y. and Shakun, M. F. (1976). Policy Sciences: Methodology and Cases. Oxford: Pergammon Press, p. 313.
http://lib.stat.cmu.edu/DASL/Datafiles/airpullutionfiltersdat.html

"Cars." From Henderson, H. V. and Velleman, P. F. (1981). "Building Regression Models Interactively". Biometrics, 37, pp. 391-411. Data originally collected from Consumer Reports.
http://lib.stat.cmu.edu/DASL/Datafiles/Cars.html

"CEO Salaries." From Forbes, November 8, 1993.
"America's Best Small Companies".
http://lib.stat.cmu.edu/DASL/Datafiles/ceodat.html

"Crews." From Hand, D. J. (1994). A Handbook of Small Data Sets. London: Chapman & Hall, p. 337.
http://lib.stat.cmu.edu/DASL/Datafiles/Crews.html

"Economics of Cities." From Union Bank of Switzerland. "Prices and earnings around the globe Economic Research Department". Zurich.
http://lib.stat.cmu.edu/DASL/Datafiles/Cities.html

"Friday the 13th." From Scanlon, T. J., Luben, R. N., Scanlon, F. L. and Singleton, N. (1993). "Is Friday the 13th Bad For Your Health?". London: BMJ, 307, pp. 1584-1586. http://lib.stat.cmu.edu/DASL/Datafiles/Fridaythe13th.html

"Gompertz's Law." From Carey, J. R., Liedo, P., Orozco, D., and Vaupel, J. W. (1992). "Slowing of Mortality Rates at Older Ages in Large Medfly Cohorts". Los Angeles: Department of Entomology, University of California, pp. 457-461.
http://lib.stat.cmu.edu/DASL/Datafiles/Medflies.html

"Helium football." From Lafferty, M. B. (1993). "OSU scientists get a kick out of sports controversy". Columbus: The Columbus Dispatch (November, 21, 1993), B7. http://lib.stat.cmu.edu/DASL/Datafiles/Heliumfootball.html

"Home Prices." From Albuquerque Board of Realtors.
http://lib.stat.cmu.edu/DASL/Datafiles/homedat.html

"Home Runs." From Moore, D. S. and McCabe, G. P. (1989). Introduction to the Practice of Statistics. New York: W. H. Freeman & Company. http://lib.stat.cmu.edu/DASL/Datafiles/HomeRuns.html

"Militiamen Chests." From Velleman, P. F. and Hoaglin, D. C. (1981). Applications, Basics, and Computing of Exploratory Data Analysis. CA: Wadsworth.

"Nursing Home Data." From These data are part of the data analyzed in Smith, H. L., Piland, N. F. and Fisher, N. (1992). "A Comparison of Financial Performance, Organizational Character-istics, and Management Strategy Among Rural and Urban Nursing Facilities".
Journal of Rural Health, Winter, pp. 27-40.
http://lib.stat.cmu.edu/DASL/Datafiles/nursinghomedat.html

"OECD Economic Development." From Singleman, J. (1978). Agriculture to Services, Sage, p. 11. http://lib.stat.cmu.edu/DASL/Datafiles/oecdat.html

"Oil Production." From Moore, D. S., and McCabe, G. P. (1989). Introduction to the Practice of Statistics. New York: W. H. Freeman & Company.
http://lib.stat.cmu.edu/DASL/Datafiles/Oilproduction.html

"Parking Meter Theft." From Finkelstein, M. O. and Levin, B. (1990). Statistics for Lawyers. New York: Springer-Verlag, p. 37-41.
http://lib.stat.cmu.edu/DASL/Datafiles/brinkdat.html

"Taste Test Scores." From Street, E. and Carroll, M. G. (1972). "Preliminary Evaluation of a Food Product", in Statistics: A Guide to the Unknown (Tanur, J. M. Ed.) Holden-Day, San Francisco, pp. 220-238.
http://lib.stat.cmu.edu/DASL/Datafiles/tastedat.html

"US Temperatures." From Hand, D. J. (1994). A Handbook of Small Data Sets. London: Chapman & Hall, pp. 208-210.
http://lib.stat.cmu.edu/DASL/Datafiles/USTemperatures.html

"Women in the Labor Force." From United States Department of Labor Statistics.
http://lib.stat.cmu.edu/DASL/Datafiles/LaborForce.html

Hand, D. J. (1994). A Handbook of Small Data Sets. London: Chapman & Hall.

Montgomery, D. C. (2008). Statistical Quality Control a Modern Introduction. New York: John Wiley & Sons, Inc.

Ruskeepaa, H. (2009). Mathematica Navigator: Mathematics, Statistics, and Graphics. New York: Academic Press.

Sheskin, D. J. (2003). Handbook of Parametric and Nonparametric Statistical Procedures. New York: Chapman and Hall/CRC.

William, Q. M. and Luis, A. E. (1998). Statistical Methods for Reliability Data. New York: John Wiley & Sons, Inc.

Wolfram Research (2011). Mathematica 文件中心。
http://reference.wolfram.com/mathematica/guide/Mathematica.html

資料陣列整理：
http://reference.wolfram.com/mathematica/guide/ListManipulation.html

資料數據與表格：
http://reference.wolfram.com/mathematica/guide/ComputableDataOverview.html
http://reference.wolfram.com/mathematica/tutorial/TablesAndMatrices.html

統計圖形應用：
http://reference.wolfram.com/mathematica/guide/StatisticalVisualization.html

數據模擬：
http://reference.wolfram.com/mathematica/tutorial/RandomNumberGeneration.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/ProbabilityDistribution.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

迴歸模型分析：
http://reference.wolfram.com/mathematica/guide/StatisticalModelAnalysis.html
http://reference.wolfram.com/mathematica/ANOVA/tutorial/ANOVA.html

集群分析：
http://reference.wolfram.com/mathematica/guide/DataClassification.html