參考文獻 |
[1] Ahrens, J. H. and Dieter, U. (1974). “Computer Methods for Sampling from Gamma, Beta, Poisson and Binomial Distributions.” Computing, 12, 223-246.
[2] Ahrens, J. H. and Dieter, U. (1982). “Generating Gamma Variates by a Modified Rejection Technique.” Communications of the ACM, 25, 47-54.
[3] Alam, K., Abernathy, R., and L., W. C. (1993). “Multivariate Goodness-of-Fit Tests Based on Statistically Equivalent Blocks.” Communications in Statistics. Theory and Methods, 22, 1515-1533.
[4] Anderson, T. W. (1966). “Some Nonparametric Procedures Based on Statistically Equivalent Blocks.” Proceedings of International Symposium on Multivariate Analysis, pp. 5-27.
[5] Best, D. J. (1983). “A Note on Gamma Variate Generators with Shape Parameter Less Than Unity.” Computing, 30, 185-188.
[6] Chatfield, C. and Goodhardt, G. (1975). “Results Concerning Brand Choice.” Journal of Marketing Reseach, 12, 110-113.
[7] Cheng, R. (1977). “The Generation of Gamma Variables with Non-integral Shape Parameters.” Applied Statistics, 26, 71-75.
[8] Connor, R. J. and Mosimann, J. E. (1969). “Concepts of Independence of Proportions with a Generalization of the Dirichlet Distribution.” Journal of the American Statistical Association, 64, 194-206.
[9] Fishman, G. (1978). Principles of Discrete Event Simulation. John Wiley & Sons Inc.
[10] Foutz, R. V. (1980). “A Test for Goodness-of-Fit Based on Empirical Probability Measure.” Annals of Statistics, 8, 989-1001.
[11] Fraser, R. V. (1957).NonparametricMethods in Statistics.Wiley Series in Statistics.
[12] Gupta, R. D. and Richards, D. S. P. (2001). “The History of the Dirichlet and Liouville Distributions.” International Statistical Review, 69, 433-446.
[13] Hogg, R. V. and Craig, V. A. (1978). Introduction to Mathematical Statistics (4th Edition). Macmillan & Company, New York.
[14] Huillet, T. and Paroissin, C. (2009). “Sampling from Dirichlet Partitions: Estimating the Number of Species.” Environmetrics, Doi: 10.1002/env.977.
[15] Hung, Y. C., Balakrishnan, N., and Lin, Y. T. (2009). “Evaluation of Beta Generation Algorithms.” Communications in Statistics - Simulation and Computation, 38, 750-770.
[16] IMSL (1980). InternationalMathematical and Statistical Libraries. Houston, Texas.
[17] J ¨ohnk, M. D. (1964). “Erzeugung von Betaverteilten und Gammaverteilten Zufallszahlen.” Metrika, 8, 5-15.
[18] Kotz, S., Balakrishnan, N., and Johnson, N. L. (2000). Continuous Multivariate Distributions, Volume 1, Methods and Applications (2nd Edition). Wiley's Series in Probability and Statistics.
[19] Lange, K. (2005). “Applications of Dirichlet Distribution to Forensic Match Probabilities.” Genetica, 96, 107-117.
[20] Loukas, S. (1984). “Simple Methods for Computer Generation of Bivariate Beta Random Variables.” Journal of Statistical Computation and Simulation, 20, 145-152.
[21] Madsen, R. E., Kauchak, D., and Elkan, C. (2005). “ModelingWord Burstiness Using the Dirichlet Distribution.” Proceedings of the 22th International Conference on Machine Learning, pp. 545-552.
[22] Marsaglia, G. and Tsang,W.W. (2001). “A SimpleMethod for Generating Gamma Variables.” ACM Transactions on Mathematical Software, 26, 363-372.
[23] Martin, J. J. (1967). Bayesian Decision Problem and Markov Chains. John Wiley & Sons, New York.
[24] Mosimann, J. E. (1962). “On the Compound Multinomial Distribution, the Multivariate Beta-Distribution and Correlations among Proportions.” Biometrica, 49, 65-82.
[25] Narayanan, A. (1990). “Computer Generation of Dirichlet Random Vectors.” Journal of Statistical Computation and Simulation, 36, 19-30.
[26] Sakasegawa, H. (1983). “Stratified Rejection and Squeeze Method for Generating Beta Random Numbers.” Annals of the Institute of Statistical Mathematics Part B, 35, 291-302.
[27] Saltelli, A., Tarantola, S., Compolongo, F., and Ratto, M. (2004). Sensitivity Analysis in Practice: A Guide to Accessing Scientific Models. John Wiley & Sons.
[28] Schmeiser, B. W. and Babu, A. J. G. (1980). “Beta Variate Generation via Exponential Majorizing Functions.” Operations Research, 28, 917-926.
[29] Serfling, R. J. (1980).Approximation Theorems forMathematical Statistics.Wiley's Series in Probability and Statistics.
[30] Tanizaki, H. (2008). “A Simple Gamma Random Number Generator for Arbitrary Shape Parameters.” Economic Bulletin, 3, 1-10.
[31] Tsui, K. W., Matsumura, E. M., and Tsui, K. L. (1985). “Multinomial-Dirichlet Bounds for Dollar Unit Sampling in Auditing.” Accounting Review, 60, 76-96.
[32] Tukey, J. W. (1947). “Non-Parametric Estimation II. Statistically Equivalent Blocks and Tolerance Regions - The Continuous Case.” The Annals of Mathematical Statistics, 18, 529-539.
[33] Wilks, S. S. (1962).Mathematical Statistics. Princeton University Press.
[34] Zechner, H. and Stadlober, E. (1993). “Generating Beta Variates via Patchwork Rejection.” Computing, 50, 1-18.
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