Page 407 - Fundamentals of Probability and Statistics for Engineers

390 Subject Index

Extreme-value distribution, 226, Lognormal distribution, 209–212, 236
type I, 228, 237 mean, 211, 236
type II, 233, 237 variance, 211, 236
type III, 234, 237
MacLaurin series, 99
F a ilure rate, see H a za rd function Markovian property, 27
Fisher–Neyman factorization criterion, 275 Markov’s inequality, 115
Frequency diagram, 248 M a ss function, seeProbability mass function

Function of random variables, 119, 137 Maximum likelihood estimate, 288
moments, 134 Maximum likelihood estimator, 288–289
probability distributions, 120 consistency, 289
efficiency, 289
Gamma distribution, 212–215, 236
mean, 213, 236 invariance property, 290
variance, 213, 236 Mean, 76–77
Gaus–Markov theorem, 345 conditional, 84
G a ussian dist ribution, see N ormal Median, 76
distribution Mode, 78
Geometric distribution, 167, 184 Moment, 76, 78
mean, 168, 184 central, 79
variance, 168, 184 joint, 87
Gumbel’s extreme value, 228 joint central, 87
distribution, 228 Moment estimate, 278
Moment estimator (ME), 278–280
Hazard function, 218 combined, 284
Histogram, 248 consistency, 279
cumulative, 327 Moment-generating function, 112, 117
Hypergeometric distribution, 167, 184 Multinomial distribution, 172, 184
mean, 184 covariance, 173
variance, 184 mean, 173, 184
H ypothesis t esting, see Test of hypothesis variance, 173, 184
Mutual exclusiveness, 13
Independence, 19–20
mutual, 18 Negative binomial distribution, 169, 184
Interarrival time, 215 mean, 171, 184
variance, 171, 184
Jacobian, 149
Normal distribution, 107, 196–199, 236
Kolmogorov–Smirnov test, 327 bivariate, 111
characteristic function, 198
Law of large numbers, 96 mean, 198, 236
Least-square estimator, 354–355 multivariate, 205
covariance, 356 standardized, 201
linear unbiased minimum variance, 344 table, 369
mean, 355 variance, 198, 236
variance, 355 Normal equation, 338
Likelihood equation, 288 Nuisance parameter, 284
Likelihood function, 288
Linear regression, 335 Parameter estimation, 259
multiple, 354 interval estimation, 294–295
other models, 357 maximum likelihood method, 287
simple, 335 moment method, 278
variance, 343 point estimation, 277

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