Index

A

Addition theorem on probability, 100
Alternative hypothesis, 15, 339–340, 340, 341, 342–343, 343, 421
Area under standard normal curve, 244
Arithmetic mean, 3, 39–51, 43, 43, 173–174, 177, 495
Average, 38
combined, 46, 492
weighted, 492, 524

B

Baye’s theorem, 105–112
Bernoulli trial, 191
Beta distribution of first kind, 276–277
Beta distribution of second kind, 277
Binomial distribution, 9, 12–14, 188, 190–191, 191, 193–195, 195, 196–210, 211, 271–274

C

Certain event, 101
Characteristics of a Binomial distribution, 196–210
Chi-square distribution, 2, 3, 22, 346, 383, 385–386, 387, 405
Chi-square test, 22–23, 346, 383, 392, 392–413
Coefficient of correlation, 293, 294–295, 294–295, 295, 311
Coefficient of determination, 311
Coefficient of nondetermination, 311
Coefficient of range, 76
Coefficient of variance, 87
Conditional probability, 102, 139, 144–149
Confidence interval, 349
Continuous random variable, 125, 128–134, 141–142, 142, 237, 275
Critical region, 341
Curve fitting, 281
Cyclic variation, 465–466, 468

D

Degrees of freedom, 391
Discrete random variable, 115, 115–119, 136, 136–137, 137–139
Dispersion, 4–5, 74–76, 75–76
Distribution function φ(Z) of standard normal variate, 243

E

Errors, 15, 32, 344
Exclusive events, 94
Expectation, 149–172, 150–154, 150

F

Fischer’s index number, 519–520, 520
Fitting a parabola by the method of least squares, 285–288
Fitting of binomial distribution, 192
Free-hand method, 467, 472

G

Gamma distribution, 275–276
Gamma distribution of second kind, 276
Geometric mean, 62–66, 63, 63–66, 495

H

Harmonic mean, 66–71, 66, 67, 495
Hypothesis, 15–23, 22, 23, 339, 339, 339–340, 340, 340, 341, 345, 345–346, 457

I

Impossible event, 95
Independent events, 101
Irregular variations, 466

K

Kurtosis, 176–182, 177, 193–195

L

Laspeyre’s price index numbers, 498–500
Least square method, 476
Level of significance, 15, 17, 18, 340, 341, 345

M

Mathematical model for a time series, 466
Mean deviation, 81–85, 82–84, 84, 84, 85, 249–259
Mean of Gamma distribution, 276
Mean of normal distribution, 245
Moment generating function of the uniform distribution, 239–241
Moment of a Poisson distribution, 214–216
about an arbitrary number, 174–175
Moments of the uniform distribution, 238–239
Moving average method, 471–474, 472–474
Multiplication theorem on probability, 103–104

N

Negative binomial distribution, 235–236, 236, 236, 236
Null hypothesis, 15, 17, 20, 340, 340, 345, 459

O

One tailed test, 341–344, 420

P

Paasche’s index numbers, 508–511
Poisson distribution, 2, 3, 14, 210–234, 211, 211, 213, 214–216, 217, 217, 217–234
Poisson Probability function, 211–213, 212–213, 213
Probability, 5, 93, 95–96, 95, 95, 96, 96–99, 99–101, 103–104
Probability distribution, 114, 114, 115–119, 136, 139, 142, 188–210, 190, 190, 210–211, 237–241
Probability of failure, 96, 121, 189
Probable error, 329
Properties of normal curve, 244–245

Q

Quartile, 71–72, 71–74, 81, 81, 177
Quartile deviation, 78–81, 78–81, 81, 81

R

Random sampling, 332, 333, 333–334
Range, 76–77, 76, 76, 76, 76–77
Regression, 293, 305–306, 306, 306, 309–311, 323
Regression coefficients, 308
Regression equation, 109, 306, 307–309, 308–309, 323, 324

S

Sample, 331, 333
Sampling, 28, 331, 332, 335
Scatter diagram, 295–296
Seasonal variation, 465
Secular trend, 465, 467
Semi average method, 468–470, 470f, 471
Skewness, 11, 176–182, 177, 193–195, 235
Spearman’s rank correlation coefficient, 301–304
Standard deviation, 4, 5, 5, 7, 49, 85–91, 87, 87, 88–91, 345, 359, 385, 415
Standard error, 7, 87, 336
Standard normal variable, 242–243

T

Test of significance for difference of means of two large samples, 352–358
Trend, 465
Two tailed test, 341–344, 342–344, 343, 343f, 420, 420
Type 1 error, 15, 15, 16, 16–17, 17, 17, 21
Type 2 error, 15, 15, 16, 16–17, 17, 17

U

Uniform distribution, 22, 235, 235, 237–241, 238, 238–239, 239, 239–241

V

W

Weibull distribution, 277–279, 278, 278

Z

Z-test, 346
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