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Introduction to Statistics by Ewa Paszek - HTML preview
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Introduction to Statistics
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Introduction to Statistics
Table of Contents
Chapter
1
.
Discrete Distributions
1.1
.
DISCRETE DISTRIBUTION
DISCRETE DISTRIBUTION
RANDOM VARIABLE OF DISCRETE TYPE
1.2
.
MATHEMATICAL EXPECTATION
MATHEMATICAL EXPECTIATION
1.3
.
THE MEAN, VARIANCE, AND STANDARD DEVIATION
The MEAN, VARIANCE, and STANDARD DEVIATION
MEAN and VARIANCE
1.4
.
BERNOULLI TRIALS and the BINOMIAL DISTRIBUTION
BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION
Bernoulli distribution
1.5
.
GEOMETRIC DISTRIBUTION
GEOMETRIC DISTRIBUTION
1.6
.
POISSON DISTRIBUTION
POISSON DISTRIBUTION
Chapter
2
.
Continuous Distributions
2.1
.
CONTINUOUS DISTRIBUTION
CONTINUOUS DISTRIBUTION
RANDOM VARIABLES OF THE CONTINUOUS TYPE
2.2
.
THE UNIFORM AND EXPONENTIAL DISTRIBUTIONS
THE UNIFORM AND EXPONENTIAL DISTRIBUTIONS
The Uniform Distribution
An Exponential Distribution
2.3
.
THE GAMMA AND CHI-SQUARE DISTRIBUTIONS
GAMMA AND CHI-SQUARE DISTRIBUTIONS
Gamma Distribution
SUMMARIZING
Chi-Square Distribution
2.4
.
NORMAL DISTRIBUTION
NORMAL DISTRIBUTION
Proof of the p.d.f. properties
2.5
.
THE t DISTRIBUTION
THE t DISTRIBUTION
THE t DISTRIBUTION
Chapter
3
.
Estimation
3.1
.
Estimation
ESTIMATION
Properties of Estimators
Method of Moments
3.2
.
CONFIDENCE INTERVALS I
CONFIDENCE INTERVALS I
3.3
.
CONFIDENCE INTERVALS II
CONFIDENCE INTERVALS II
Confidence Intervals for Means
Confidence Interval for Variances
3.4
.
SAMPLE SIZE
Size Sample
3.5
.
Maximum Likelihood Estimation (MLE)
MAXIMUM LIKELIHOOD ESTIMATION (MLE)
Likelihood function
Maximum Likelihood Estimation
3.6
.
Maximum Likelihood Estimation - Examples
MAXIMUM LIKELIHOOD ESTIMATION - EXAMPLES
EXPONENTIAL DISTRIBUTION
GEOMETRIC DISTRIBUTION
NORMAL DISTRIBUTION
BINOMIAL DISTRIBUTION
POISSON DISTRIBUTION
3.7
.
ASYMPTOTIC DISTRIBUTION OF MAXIMUM LIKELIHOOD ESTIMATORS
ASYMPTOTIC DISTRIBUTION OF MAXIMUM LIKELIHOOD ESTIMATORS
Chapter
4
.
Tests of Statistical Hypotheses
4.1
.
TEST ABOUT PROPORTIONS
TEST ABOUT PROPORTIONS
EXAMPLE
4.2
.
TESTS ABOUT ONE MEAN AND ONE VARIANCE
TESTS ABOUT ONE MEAN AND ONE VARIANCE
4.3
.
TEST OF THE EQUALITY OF TWO INDEPENDENT NORMAL DISTRIBUTIONS
TEST OF THE EQUALITY OF TWO INDEPENDENT NORMAL DISTRIBUTIONS
4.4
.
BEST CRITICAL REGIONS
BEST CRITICAL REGIONS
4.5
.
HYPOTHESES TESTING
Hypotheses Testing - Examples.
Chapter
5
.
Pseudo - Numbers
5.1
.
PSEUDO-NUMBERS
UNIFORM PSEUDO-RANDOM VARIABLE GENERATION
CURRENT ALGORITHMS
5.2
.
PSEUDO-RANDOM VARIABLE GENERATORS, cont.
PSEUDO-RANDOM VARIABLE GENERATORS, cont.
A Shift-Register Generator
Fibonacci Generators
Combinations of Generators (Shuffling)
5.3
.
THE IVERSE PROBABILITY METHOD FOR GENERATING RANDOM VARIABLES
THE IVERSE PROBABILITY METHOD FOR GENERATING RANDOM VARIABLES
The Continuous Case
The Discrete Case
Index
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