734 Index
Bernoulli distribution, 155
mean, 155
variance, 155
Bernoulli experiment, 155
Bernoulli trials, 155
Best critical region, 470
Neyman–Pearson Theorem, 472
Beta distribution, 181
generation, 303
mean, 181
relationship with binomial, 185
variance, 181
Big O notation, 335
Bigler, E., 237
Binomial coefficient, 17
Binomial distribution, 156
additive property, 159
arcsin approximation, 346
continuity correction, 345
mean, 157
mgf, 157
mixture generalization, 221
normal approximation, 344
Poisson approximation, 337
relationship with beta, 185
variance, 157
Birthday problem, 16
Bisection algorithm, 249
Bivariate normal distribution, 198
Bonferroni Procedure, 526
Bonferroni procedure, 526
Bonferroni’s inequality, 20
Boole’s inequality, 19
Bootstrap, 303
hypotheses test
for Δ =μY−μX, 309
hypotheses testing
forμ, 311
nonparametric, 445
parametric, 445
percentile confidence interval
forθ, 305
standard errors, 444
standardized confidence interval, 313
Borelσ-field, 23
Bounded in probability, 333
implied by convergence in distribu-
tion, 333
Box, G. E. P., 296
Boxplot, 259
adjacent points, 259
lower fence, 259
potential outliers, 259
upper fence, 259
Bray, T. A., 297, 303
Breakdown point, 644
sample mean, 644
sample median, 645
Breiman, L., 336
Burr distribution, 222
hazard function, 223Canty, A., 636
Capture-recapture, 165
Carmer, S.G., 528
Casella, G., 300, 386, 393, 452, 457, 676,
678, 679, 681, 682
Cauchy distribution, 60, 67, 73
mgf does not exist, 73
relationship witht-distribution, 217
cdf,seeCumulative distribution function
(cdf)
n-variate, 134
joint, 86
Censoring, 56
Central Limit Theorem, 342
n-variate, 351
normal approximation to binomial,
344
statement of, 240
Characteristic function, 74
Chebyshev’s inequality, 79
Chi-square distribution, 178
kth moment, 179
additive property, 180
mean, 178
normal approximation, 338
relationship with multivariate nor-
mal distribution, 202
relationship with normal, 192
variance, 178
Chi-square tests, 283
Chung, K. L., 70, 322
Combinations, 17
Complement, 4
Complete likelihood function, 405
Complete sufficient statistic, 433
exponential class, 435
Completeness, 431
Lehmann and Scheff ́e theorem, 432
Composite hypothesis, 270
Compounding, 220
Concordant pairs, 632
Conditional distribution
n-variate, 136
continuous, 110
discrete, 110
Conditional probability, 24
Confidence coefficient, 239
Confidence interval, 31, 238
μ 1 −μ 2
t-interval, 243