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Mathematical Statistics
- Introduction to Mathematical Statistics
- Basic Notions and Problems of Mathematical Statistics
- Basic problems of mathematical statistics.
- Population and sample.
- Theoretical distribution function.
- Simplest Statistical Transformations
- Series of order statistics.
- Statistical series.
- Interval series.
- Relative frequencies.
- Notion of statistic.
- Empirical distribution function.
- Graphical representation of statistical distribution.
- Main distributions of mathematical statistics.
- Numerical Characteristics of Statistical Distribution
- Statistical Estimation
- Estimators and Their Properties
- Notion of estimator.
- Unbiased estimators.
- Efficiency of estimators.
- Consistency of estimators.
- Sufficient estimators.
- Main statistical estimators.
- Estimation Methods for Unknown Parameters
- Interval Estimators (Confidence Intervals)
- Statistical Hypothesis Testing
- References for Chapter 21
Abstract
The term “statistics” derives from the Latin word “status,” meaning “state.” Statistics comprises three major divisions: collection of statistical data, their statistical analysis, and development of mathematical methods for processing and using the statistical data to draw scientific and practical conclusions. It is the last division that is commonly known as mathematical statistics.
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