REFERENCES AND FURTHER STUDIES

Transcription

1 REFERENCES AND FURTHER STUDIES by..0. on /0/. For personal use only.. Afifi, A. A., and Azen, S. P. (), Statistical Analysis A Computer Oriented Approach, Academic Press, New York.. Alvarez, A. R., Welter, D. J., and Johnson, M. (), "Problem Solving in the IC Industry Through Applied Statistics: Comparing Two Processes," Solid State Technology, pp. -.. Box, G. E. P. and Muller, M. E. (), "A Note on Generating of Normal Deviates,",wi. Math. Stat, pp David, H. A. (), Order Statistics, John Wiley & Sons, New York.. Duran, J. W., and Wiorkowski, J. J. (0), "Quantify Software Validity by Sampling," IEEE Transactions on Reliability, pp. -.. Edgington, E. S. (0), Randomization Tests, Marcel Dekker, New York.. Efron, B. (), The Jackknife, the Bootstrap and Other Resampling Plans, SIAM Press, Philadelphia.. Feller, W. (), An Introduction to Probability Theory and Its Applications, Vol. I, John Wiley & Sons, New York.. Goodman, L. A. (), "Serial Number Analysis," Journal of American Statistical Association, pp. -.

2 Understanding and Learning Statistics by Computer 0. Gay, F. A. (), "Evaluation of Maintenance Software in Real-Time System," IEEE Transactions on Computers, pp. -.. Huber, P. J. (), Robust Statistical Procedures, SIAM Press, Philadelphia. by..0. on /0/. For personal use only.. Johnson, N. L. and Kotz, S. (), Discrete Distributions, John Wiley & Sons, New York.. Johnson, N. L.andKotz,S.(0),Continuous UnivariateDistributions-, John Wiley & Sons, New York.. Kennedy, W. J., and Gentle, J. E. (0), Statistical Computing, Marcel DEkker, New York.. McClave, J. T., and Dietrich, F. H. (\S),Statistics, Dellen, San Francisco.. Mendenhall, W., Scheaffer, R. L., and Wackerly, D. (),Mathematical Statistics with Applications, Duxbury Press, North Scituate, Mass.. Myers, G. J. (), Software Reliability, Principles and Practices, John Wiley & Sons, New York.. Rubinstein, R. Y. (), Simulation and the Monte Carlo Method, John Wiley & Sons, New York.. Scheaffer, R. L. and McClave. J. T.(), Statistics for Engineers, Duxbury Press, Boston. 0. Trivedi, K. S. (), Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Prentice-Hall, New Jersey.. Vitter, J. S. (), "Optimal Algorithm for Random Sampling Problems," IEEE Fundamental of Computers, pp. -.

3 Appendices Tables Table A.l Thez-table. F(:»-L y/r e~»" dt by..0. on /0/. For personal use only. X F(x) Fix) X F(x) F{x) X Fix) / Fix)

4 Understanding and Learning Statistics by Computer Table A.l (continued) Fix) - F(x) X F(x) - F(x) * Fix) - Fix) by..0. on /0/. For personal use only Q ' * S

5 Appendices - Tables Table A.l (continued) X Fix) - F(x) X Fix) - Fix) by..0. on /0/. For personal use only Reprinted with permission from CRC Handbook of Tables for Probabi lity and Statistics. Copyright by CF,C Press In c, Boca R aton, Fl orida.

6 Understanding and Learning Statistics by Computer Table A. Student's t-distribution PERCENTAGE POINTS, STUDENTS ^-DISTRIBUTION "' I'M^y* by..0. on /0/. For personal use only. r ^ Reprinted with permission from CRC Handbook of Tables for Probability and Statistics. Copyright by CRC Press Inc., Boca Raton, Florida.

7 by..0. on /0/. For personal use only Table A. PERCENTAGE POINTS, CHI-SQUARE DISTRIBUTION Fix*) ['-A-,*-? ^ * h *r(?) Rep rinted with permission from Q KCHand book of Tables for Probability and Statistics. Copyright by CRC Press Inc. Boca Rate n, Florida e * dx ^ -Q g- O- 00

8 by..0. on /0/. For personal use only. ^ F ? - Sl 0.00, ' r F(F) " ( Table A. PERCENTAGE POINTS, tn + n n m ^ - ^-m* r- TO n z _K H in F-DISTRIBUTION. where t\ n/ «? - Si/ m and *\ - St/n ar e indepen dent mean squares e stimating a coramor i variance * and based on m and n degrees of freedom, respectively \n mi) m+n dx j I j I O s I " * Q, t- S* < Co CO* O* C* o ««$

9 v by..0. on /0/. For personal use only * F = I a* ml where n F(F) Table A. (continued) PERCENTAGE POINTS, F-DISTRIBUTION ff T(^^) * -, ± \ * / (fho ?x (n + mx) S? - Si/ m and s\ = Si/n ar t indepenc ent mean squares e sttmating a common variance a and hased on m and n degrees of freedom, respectively IS m +n dx = I L 00 ^ * v

10 by..0. on /0/. For personal use only. ^ s t i 0 IS IS SO a Table A. (continued) PERCENTAGE POINTS, F-DISTRIBUTION ( m + n \ m n m m+n F(F) > * An?n*z (n + mx)~ «)' - ( ' $ dx »M '-rj/r- k?-*/-!-*/.. D squares estiraataf a e B variance #» and baaed on w and a degrees of freedom, respectively. Reprinted with permission from CRC Handbook of Tables for Probability and Statistics. Copyright by CRC Press Inc., Boca Raton, Florida SO S St I'

11 Appendices Tables Table A. The Binomial Tablep(x) = (*) d x (l-d) n ~ INDIVIDUAL TERMS, BINOMIAL DISTRIBUTION n x e by..0. on /0/. For personal use only Linear interpolations with respect to 0 will in general be accurate at most to two decimal places.

12 Understanding and Learning Statistics by Computer Table A. (continued) INDIVIDUAL TERMS, BINOMIAL DISTRIBUTION n x 0 I e * by..0. on /0/. For personal use only.

13 Appendices Tables Table A. (continued) INDIVIDUAL TERMS, BINOMIAL DISTRIBUTION e n x by..0. on /0/. For personal use only (KX)

14 Understanding and Learning Statistics by Computer Table A. (continued) INDIVIDUAL TERMS, BINOMIAL DISTRIBUTION n x e OOOO by..0. on /0/. For personal use only.

15 Table A. (continued) INDIVIDUAL TERMS, BINOMIAL DISTRIBUTION Appendices Tables n x e by..0. on /0/. For personal use only oooo' i Reprinted with permission from CRC Handbook of Tables for Probability and Statistics. Copyright by CRC Press Inc., Boca Raton, Florida.

16 Understanding and Learning Statistics by Computer Table A. Random Numbers (The first decimals). Line/Col () H () () (> () () () () i () I (0) () () () () I Reprinted with permission from CRC Handbook of Tables for Probability and Statistics. Copyright by CRC Press Inc., Boca Raton, Florida. by..0. on /0/. For personal use only.

17 Table A. Standard Normal Deviates (M = 0, o = ). Appendices Tables by..0. on /0/. For personal use only , C Reprinted with permission from CRC Handbook of Tables for Probability and Statistics. Copyright by CRC Press Inc., Boca Raton, Florida.

18 by..0. on /0/. For personal use only. This page is intentionally left blank

19 INDEX by..0. on /0/. For personal use only. acceptance-rejection method bootstrap 0 Central Limit Theorem confidence interval, contingency table correlation correlation fallacy cumulative distribution function (CDF), cumulative frequency 0 data distribution Bernoulli beta 0 binomial, chi-square, Erlang exponential F, gamma geometric hypergeometric normal,,, normal, bivariate Poisson t, uniform, efficiency of estimator frequency table statistical inference 0 histogram hypothesis testing, alternative hypothesis composite null hypothesis p-value, risk in simple Type I error Type II error invariant statistic inverse CDF method jackknife 0 least squares estimator linear congruential generator maximum concentration criterion 0 maximum likelihood estimation 0 mean mean, statistical inference one sample two sample paired sample

20 0 Understanding and Learning Statistics by Computer by..0. on /0/. For personal use only. minimum variance unbiased estimator (MVUE) modulus operation moments Monte Carlo integration 0 Monte Carlo method no nparametric inference 0,0 permutation test Poisson process population probabilistic algorithm 0 probability, axiom of conditional probability density function (PDF) proportion, statistical inference quicksort random number subset variable regression robust inference 0,0 sample mean median 00,0 sample size determination for confidence interval for hypothesis testing software reliability trimmed mean 0 unbiased estimator variance statistical inference

21 Answers to Selected Exercises by..0. on /0/. For personal use only. Exercise.,,. No, it can generate at most different numbers.. See whether it is uniform.. (iii) 0,.,..,0. No integer division is used for modulus operation.. S= {(i, j) i, j =,,,,, } (a) / (b) / (c) / (d) /. (a) / (b) /. (a) /,000 (b) /0. (a) 0. (b) 0. Exercise. JU =., a =.. (0., 0.), (0., 0.), (0., 0.). (a) 0. (b). 0 = (i) 0. (ii) 0. (iii) 0. (iv) 0. (v) /X. e' '. Pr{Waiting time longer than T} = Pr {No call in the interval [ 0, T ]}. Ag. average time: Agl =., Ag =.. (i) (ii) (iii) (iv) (Your answer may differ some.). (i) Acceptance-rejection (ii) Inverse CDF (ii) Acceptance-rejection Exercise. (0.,0.).. No. Riskprob. = 0.. Yes. Riskprob. = (a) risk = 0.0 (b) risk = 0.

22 0 Understanding and Learning Statistics by Computer. (a) p-value = 0.0 (b) H 0 : p x = p =... = Pio = /0, /f : One of them is not /0. The risk probability can be found by simulation. It is (i) 0. (ii) Use Poisson 0. (iii) Use normal (a) 0. (b) 0.00 (c) n =, c = by..0. on /0/. For personal use only. Exercise. (i = x,d =(n-\)s /n. (i) No. (ii) is not a good measure of the mean direction.. Yes.. Yes.. They can be reduced to two parameters. Exercise. p = 0.0. ±.. 0. ±0.0. None is significant at 0.0 level.. Mean interval is robust against non-normality, but the variance interval is not.. Q = 0., p < Q =., p < The breakdowns are not random..0 Q =., p< y = -. +.JC, ft is significantly different from 0(p < 0.0).. Pi = 0., p = 0. both significant at 0.0 level.. p = p= 0. Exercise. (i) \/N (ii) n/n. (n - l)/(n + ), Store the largest so far in the memory and replace the smaller one if x(n + ) is larger. Expected # of comparisons = W+n(V). n - l /n\ ~(e/n) n. No, the data may be partially ordered. The first one may be very far away from the median.. (i) 0.00 (ii) 0...