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題名 R軟體套件"rBeta2009"之評估及應用
Evaluation and Applications of the Package "rBeta2009"
作者 劉世璿
Liu, Shih Hsuan
貢獻者 洪英超
Hung, Ying Chao
劉世璿
Liu, Shih Hsuan
關鍵詞 狄氏分配
貝他分配
有效性
精確性
隨機性
beta variates
Dirichlet random vectors
efficiency
accuracy
randomness
日期 2011
上傳時間 30-Oct-2012 10:41:01 (UTC+8)
摘要 本論文主要是介紹並評估一個R的軟體套件叫做"rBeta2009"。此套件是由Cheng et al. (2012) [8] 所設計，其目的是用來產生貝他分配(Beta Distribution)及狄氏分配(Dirichlet Distribution)的亂數。本論文特別針對此套件之(i)有效性(effiniency)、(ii)精確性(accuracy)及(iii)隨機性(randomness)進行評估，並與現有的R套件作比較。此外，本論文也介紹如何應用此套件來產生(i)反貝他分配(Inverted Beta Distribution)、(ii)反狄氏分配(Inverted Dirichlet Distribution)、(iii)Liouville分配及(iv)凸面區域上的均勻分配之亂數。
A package in R called "rBeta2009", originally designed by Cheng et al. (2012) [6], was introduced and evaluated in this thesis. The purpose of the package is generating beta random numbers and Dirichlet random vectors. In this paper, we not only evaluated (i) the efficiency, (ii) the accuracy and (iii) the randomness, but also compare it with other R packages currently in use. In addition, it was also scrutinized in this thesis how to generate (i) inverted beta random numbers, (ii) inverted Dirichlet random vectors, (iii) Liouville random vectors, and (iv) uniform random vectors over convex polyhedron by using the same package.
參考文獻 [1] A.C. Atkinson and Whittaker (1976). A Switching Algorithm for the Generation of Beta Random Variables With at Least One Parameter Less Than One. Proceedings of the Royal Society of London, Series A, 139, pp. 462-467.
[2] K. Alam, R. Abernathy and C.L.Williams (1993). Multivariate Goodness-of-Fit Tests Based on Statistically Equivalent Blocks. Communication in Statistics, Theory Methods 22, pp. 1515–1533.
[3] A.G. Ashraf and S. Tamás (2009). On Numerical Calculation of Probabilities According to Dirichlet Distribution. Annals of Operations Research, 177, pp. 185–200.
[4] T.W. Anderson (1966). Some Nonparametric Procedures Based on Statistically Equivalent Blocks. Proceedings of International Symposium on Multivariate Analysis. P.R. Krishnaiah ed., Academic Press Inc., New York, pp. 5–27.
[5] T. Bdiri and N. Bouguila (2011). Learning Inverted Dirichlet Mixtures for Positive Data Clustering. Neural Information Processing, ICONIP 2011, Part II, LNCS 7063, pp. 71–78. Springer, Heidelberg.
[6] T. Bdiri and N. Bouguila (2011). Learning Inverted Dirichlet Mixtures for Positive Data Clustering. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGrC 2011. LNCS, 6743, pp. 265–272. Springer, Heidelberg.
[7] R.C.H. Cheng (1978). Generating Beta Variates with Nonintegral Shape Parameters. Communications of the Association for Computing Machinery, 21, pp. 317-322.
[8] C.W. Cheng, Y.C. Hung and N. Balakrishnan (2012). Package "rBeta2009". URL http://cran.r-project.org/package=rBeta2009.
[9] R.V. Foutz (1980). A test for goodness of fit based on empirical probability measure. The Annals of Statistics, 8, pp. 989–1001.
[10] K.T. Fang, G.L. Tian and M.Y. Xie. (1997). Uniform Distribution on Convex Polyhedron and Its Applications. Department of Mathematics, Hong Kong Batist University, No. 149.
[11] D.A.S. Fraser (1957). Nonparametric Methods in Statistics, JohnWiley & Sons, NewYork.
[12] T. Hahn (2005). CUBA—a library for multidimensional numerical integration. Computer Physics Communications, 168, pp. 78–95.
[13] Y.C. Hung, N. Balakrishnan and Y.T. Lin (2009). Evaluation of Beta Generation Algorithms. Communications in Statistics - Simulation and Computation, 38, pp. 750-770.
[14] Y.C. Hung, N. Balakrishnan and C.W. Cheng (2011). Evaluation of Algorithms for Generating Dirichlet Random Vectors. Journal of Statistical Computation and Simulation, 81, pp. 445-459.
[15] J.R.M. Hosking (1981). Fractional Differencing. Biometrica, Vol. 68, No. 1981, pp. 165-176.
[16] J.R.M. Hosking (1980). The Multivariate Portmanteau Statistic. Journal of American Statistical Association, 75, pp. 602-608.
[17] B. Jarle and O.E. Terje (1991). An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, Vol. 17, No. 4, pp. 437-451.
[18] B. Jarle and O.E. Terje (1991). Algorithm 698: DCUHRE: An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, Vol. 17, No. 4, pp. 452-456.
[19] M.D. Jöhnk (1964). Erzeugung von betaverteilten und gammaverteilten zuffallszahlen. Metrika, 8, pp. 5-15.
[20] D.P. Kennedy (1988). A note on stochastic search methods for global optimization. Advances in Applied Probability, 20, pp. 476-478.
[21] K. Lange (2005). Applications of the Dirichlet distribution to forensic match probabilities, Genetica , 96, pp. 107–117.
[22] G. Laval, M. SanCristobal and C. Chevalet (2003). Maximum-likelihood and Markov chain Monte Carlo approaches to estimate inbreeding and effective size from allele frequency changes. Genetics, 164 (3), pp. 1189-1204.
[23] J. Liouville (1839). Note sur quelquess integrals définies. Journal de Mathématiques Pures et Appliquées, 4, pp. 225-235.
[24] G.M. Ljung and G.E.P. Box (1978). On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, pp. 297-303.
[25] R.E. Madsen, D. Kauchak and C. Elkan (2005). Modeling Word Burstiness Using the Dirichlet Distribution. Proceeding of the 22nd International Conference on Machine Learning, pp. 545-552.
[26] A.J. McNeila and J. Nešlehová (2010).From Archimedean to Liouville copulas. Journal of Multivariate Analysis, 101, 8, pp. 1772-1790.
[27] J.B. McDonald and R.J. Butler (1987). Some generalized mixture distributions with an application to unemployment duration. The Review of Economics and Statistics, 69, pp. 232–240.
[28] D.G. Rameshwar and St. P.R. Donald (1987). Multivariate Liouville distribution. Journal of Multivariate Analysis, 23, pp. 233-256.
[29] R.J. Serfling (1980). Approximation Theorems for Mathematical Statistics. JohnWiley & Sons, NewYork.
[30] B.W. Schmeiser and A.J.G. Babu (1980). Beta Variate Generation via Exponential Majorizing Functions. Operations Research, 28,pp. 917-926.
[31] K. Sjölander, K. Karplus, M. Brown, R. Hughey, A. Krogh, I. S. Mian and D. Haussler (1996). Dirichlet mixtures: A method for Improving Detection of Weak but Significant Protein Sequence Homology. The Computer Application in Bioscience, 12, pp. 327-345.
[32] H. Sakasegawa (1983). Stratified rejection and squeeze method for generating beta random numbers. Annals of the Institute Statistical Mathematics, 35,pp. 291-302.
[33] H. Sahai and R.L. Anderson (1973). Confidence regions for variance ratios of the random models for balanced data. Journal of the American Statistical Association, 68, 344, pp. 951-952.
[34] J.W. Tukey (1947). Non-parametric estimation II. Statistically Equivalent Blocks and tolerance regions – the continuous case. The Annals of Mathematical Statistics, 18, pp. 529–539.
[35] G.G. Tiao and I. Guttman (1965a). The inverted Dirichlet distribution with applications. Journal of the American Statistical Association, 60, pp. 793–805.
[36] G.G. Tiao and I. Guttman (1965b). The inverted Dirichlet distribution with applications. Journal of the American Statistical Association, 60, pp. 1251-1252.
[37] G.R. Warnes (2010). Various R programming tools. URL http://cran.r-project.org/web/packages/gtools/gtools.pdf.
[38] E.P. Xing, M.I. Jordan, R.M. Karp and S. Russell (2002). A Hierarchical Bayesian Markovian Model for Motifs in Biopolymer Sequences. Proceedings of Advances in National Information Processing Systems, pp. 1489-1496.
[39] H. Zechner and E. Stadlober (1993). Generating beta variates via patchwork rejection. Computing, 50,pp. 1-18.
描述 碩士
國立政治大學
統計研究所
99354027
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354027
資料類型 thesis
dc.contributor.advisor 洪英超zh_TW
dc.contributor.advisor Hung, Ying Chaoen_US
dc.contributor.author (Authors) 劉世璿zh_TW
dc.contributor.author (Authors) Liu, Shih Hsuanen_US
dc.creator (作者) 劉世璿zh_TW
dc.creator (作者) Liu, Shih Hsuanen_US
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 10:41:01 (UTC+8)-
dc.date.available 30-Oct-2012 10:41:01 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 10:41:01 (UTC+8)-
dc.identifier (Other Identifiers) G0099354027en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54301-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 99354027zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 本論文主要是介紹並評估一個R的軟體套件叫做"rBeta2009"。此套件是由Cheng et al. (2012) [8] 所設計，其目的是用來產生貝他分配(Beta Distribution)及狄氏分配(Dirichlet Distribution)的亂數。本論文特別針對此套件之(i)有效性(effiniency)、(ii)精確性(accuracy)及(iii)隨機性(randomness)進行評估，並與現有的R套件作比較。此外，本論文也介紹如何應用此套件來產生(i)反貝他分配(Inverted Beta Distribution)、(ii)反狄氏分配(Inverted Dirichlet Distribution)、(iii)Liouville分配及(iv)凸面區域上的均勻分配之亂數。zh_TW
dc.description.abstract (摘要) A package in R called "rBeta2009", originally designed by Cheng et al. (2012) [6], was introduced and evaluated in this thesis. The purpose of the package is generating beta random numbers and Dirichlet random vectors. In this paper, we not only evaluated (i) the efficiency, (ii) the accuracy and (iii) the randomness, but also compare it with other R packages currently in use. In addition, it was also scrutinized in this thesis how to generate (i) inverted beta random numbers, (ii) inverted Dirichlet random vectors, (iii) Liouville random vectors, and (iv) uniform random vectors over convex polyhedron by using the same package.en_US
dc.description.tableofcontents 第一章 導論 1
第二章 "rBeta2009"套件之介紹 3
第一節 生成貝他分配之演算法 3
第二節 生成狄氏分配之演算法 4
第三節 "rBeta2009"之指令執行 6
第三章 "rBeta2009"套件評估 8
第一節 有效性 (Efficiency) 8
第二節 準確性 (Accuracy) 13
第三節 隨機性 (Randomness) 17
第四章 "rBeta2009"套件之其他應用 20
第一節 生成反貝他分配(Inverted Beta Distribution)及反狄氏分配(Inverted Dirichlet Distribution) 20
第二節 生成Liouville分配 23
第三節 生成凸面區域的均勻分配 27
第五章 結論 30
參考文獻 31		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354027en_US
dc.subject (關鍵詞) 狄氏分配zh_TW
dc.subject (關鍵詞) 貝他分配zh_TW
dc.subject (關鍵詞) 有效性zh_TW
dc.subject (關鍵詞) 精確性zh_TW
dc.subject (關鍵詞) 隨機性zh_TW
dc.subject (關鍵詞) beta variatesen_US
dc.subject (關鍵詞) Dirichlet random vectorsen_US
dc.subject (關鍵詞) efficiencyen_US
dc.subject (關鍵詞) accuracyen_US
dc.subject (關鍵詞) randomnessen_US
dc.title (題名) R軟體套件"rBeta2009"之評估及應用zh_TW
dc.title (題名) Evaluation and Applications of the Package "rBeta2009"en_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] A.C. Atkinson and Whittaker (1976). A Switching Algorithm for the Generation of Beta Random Variables With at Least One Parameter Less Than One. Proceedings of the Royal Society of London, Series A, 139, pp. 462-467.
[2] K. Alam, R. Abernathy and C.L.Williams (1993). Multivariate Goodness-of-Fit Tests Based on Statistically Equivalent Blocks. Communication in Statistics, Theory Methods 22, pp. 1515–1533.
[3] A.G. Ashraf and S. Tamás (2009). On Numerical Calculation of Probabilities According to Dirichlet Distribution. Annals of Operations Research, 177, pp. 185–200.
[4] T.W. Anderson (1966). Some Nonparametric Procedures Based on Statistically Equivalent Blocks. Proceedings of International Symposium on Multivariate Analysis. P.R. Krishnaiah ed., Academic Press Inc., New York, pp. 5–27.
[5] T. Bdiri and N. Bouguila (2011). Learning Inverted Dirichlet Mixtures for Positive Data Clustering. Neural Information Processing, ICONIP 2011, Part II, LNCS 7063, pp. 71–78. Springer, Heidelberg.
[6] T. Bdiri and N. Bouguila (2011). Learning Inverted Dirichlet Mixtures for Positive Data Clustering. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGrC 2011. LNCS, 6743, pp. 265–272. Springer, Heidelberg.
[7] R.C.H. Cheng (1978). Generating Beta Variates with Nonintegral Shape Parameters. Communications of the Association for Computing Machinery, 21, pp. 317-322.
[8] C.W. Cheng, Y.C. Hung and N. Balakrishnan (2012). Package "rBeta2009". URL http://cran.r-project.org/package=rBeta2009.
[9] R.V. Foutz (1980). A test for goodness of fit based on empirical probability measure. The Annals of Statistics, 8, pp. 989–1001.
[10] K.T. Fang, G.L. Tian and M.Y. Xie. (1997). Uniform Distribution on Convex Polyhedron and Its Applications. Department of Mathematics, Hong Kong Batist University, No. 149.
[11] D.A.S. Fraser (1957). Nonparametric Methods in Statistics, JohnWiley & Sons, NewYork.
[12] T. Hahn (2005). CUBA—a library for multidimensional numerical integration. Computer Physics Communications, 168, pp. 78–95.
[13] Y.C. Hung, N. Balakrishnan and Y.T. Lin (2009). Evaluation of Beta Generation Algorithms. Communications in Statistics - Simulation and Computation, 38, pp. 750-770.
[14] Y.C. Hung, N. Balakrishnan and C.W. Cheng (2011). Evaluation of Algorithms for Generating Dirichlet Random Vectors. Journal of Statistical Computation and Simulation, 81, pp. 445-459.
[15] J.R.M. Hosking (1981). Fractional Differencing. Biometrica, Vol. 68, No. 1981, pp. 165-176.
[16] J.R.M. Hosking (1980). The Multivariate Portmanteau Statistic. Journal of American Statistical Association, 75, pp. 602-608.
[17] B. Jarle and O.E. Terje (1991). An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, Vol. 17, No. 4, pp. 437-451.
[18] B. Jarle and O.E. Terje (1991). Algorithm 698: DCUHRE: An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, Vol. 17, No. 4, pp. 452-456.
[19] M.D. Jöhnk (1964). Erzeugung von betaverteilten und gammaverteilten zuffallszahlen. Metrika, 8, pp. 5-15.
[20] D.P. Kennedy (1988). A note on stochastic search methods for global optimization. Advances in Applied Probability, 20, pp. 476-478.
[21] K. Lange (2005). Applications of the Dirichlet distribution to forensic match probabilities, Genetica , 96, pp. 107–117.
[22] G. Laval, M. SanCristobal and C. Chevalet (2003). Maximum-likelihood and Markov chain Monte Carlo approaches to estimate inbreeding and effective size from allele frequency changes. Genetics, 164 (3), pp. 1189-1204.
[23] J. Liouville (1839). Note sur quelquess integrals définies. Journal de Mathématiques Pures et Appliquées, 4, pp. 225-235.
[24] G.M. Ljung and G.E.P. Box (1978). On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, pp. 297-303.
[25] R.E. Madsen, D. Kauchak and C. Elkan (2005). Modeling Word Burstiness Using the Dirichlet Distribution. Proceeding of the 22nd International Conference on Machine Learning, pp. 545-552.
[26] A.J. McNeila and J. Nešlehová (2010).From Archimedean to Liouville copulas. Journal of Multivariate Analysis, 101, 8, pp. 1772-1790.
[27] J.B. McDonald and R.J. Butler (1987). Some generalized mixture distributions with an application to unemployment duration. The Review of Economics and Statistics, 69, pp. 232–240.
[28] D.G. Rameshwar and St. P.R. Donald (1987). Multivariate Liouville distribution. Journal of Multivariate Analysis, 23, pp. 233-256.
[29] R.J. Serfling (1980). Approximation Theorems for Mathematical Statistics. JohnWiley & Sons, NewYork.
[30] B.W. Schmeiser and A.J.G. Babu (1980). Beta Variate Generation via Exponential Majorizing Functions. Operations Research, 28,pp. 917-926.
[31] K. Sjölander, K. Karplus, M. Brown, R. Hughey, A. Krogh, I. S. Mian and D. Haussler (1996). Dirichlet mixtures: A method for Improving Detection of Weak but Significant Protein Sequence Homology. The Computer Application in Bioscience, 12, pp. 327-345.
[32] H. Sakasegawa (1983). Stratified rejection and squeeze method for generating beta random numbers. Annals of the Institute Statistical Mathematics, 35,pp. 291-302.
[33] H. Sahai and R.L. Anderson (1973). Confidence regions for variance ratios of the random models for balanced data. Journal of the American Statistical Association, 68, 344, pp. 951-952.
[34] J.W. Tukey (1947). Non-parametric estimation II. Statistically Equivalent Blocks and tolerance regions – the continuous case. The Annals of Mathematical Statistics, 18, pp. 529–539.
[35] G.G. Tiao and I. Guttman (1965a). The inverted Dirichlet distribution with applications. Journal of the American Statistical Association, 60, pp. 793–805.
[36] G.G. Tiao and I. Guttman (1965b). The inverted Dirichlet distribution with applications. Journal of the American Statistical Association, 60, pp. 1251-1252.
[37] G.R. Warnes (2010). Various R programming tools. URL http://cran.r-project.org/web/packages/gtools/gtools.pdf.
[38] E.P. Xing, M.I. Jordan, R.M. Karp and S. Russell (2002). A Hierarchical Bayesian Markovian Model for Motifs in Biopolymer Sequences. Proceedings of Advances in National Information Processing Systems, pp. 1489-1496.
[39] H. Zechner and E. Stadlober (1993). Generating beta variates via patchwork rejection. Computing, 50,pp. 1-18.		zh_TW