- Fundamentals
1.1. Goal and task of statistics
1.2. Basic terms of probability theory
1.3. Basic terms of statistical inference
- Some areas of application of mathematical statistics in mining
- Analysis of data
3.1. Testing of sample randomness
3.2. An outlier in a sample
3.3. Stationarity testing of sequences
3.4. Outcome dispersion testing
3.5. Cyclic component tracing
3.6. Autocorrelation analysis
3.7. Homogeneity of data
- Synthesis of data
4.1. Estimation of the parameters of a random variable
4.2. Probability distribution description
4.3. An example of empirical–theoretical inference about the distribution of a random variable
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Relationships between random variables
5.1. The chi-square test of independence
5.2. The Pearson’s linear correlation coefficient
5.3. Partial correlation coefficient and multiple correlation coefficient
5.4. Non-linear correlation measures
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Synthesis of data—regression analysis
6.1. Preliminary remarks
6.2. Linear regression
6.3. Linear transformations and multidimensional models
6.4. Autocorrelation and autoregression models
6.5. Classical linear regression for many variables
6.6. Regression with errors in values of random variables
6.7. Linear regression with additional information
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Special topic: Prediction
7.1. Introduction and basic terms
7.2. Subject of prediction
7.3. Examples
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Explanations of some important terms
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Statistical tables
9.1. Distribution function Φ(z) of standardised normal distribution N(0, 1).
9.2. Quantiles of the standardised normal distribution N(0, 1)
9.3. Critical values of the Student’s t-distribution
9.4. Critical values of the Chi-squared distribution
9.5. Critical values of the Snedecor’s F distribution for α = 0.10
9.6. Critical values of the Snedecor’s F distribution for α = 0.05
9.7. Critical values of the Snedecor’s F distribution for α = 0.025
9.8. Critical values of the series distribution
9.9. Critical values of the Cochran statistic for α = 0.05
9.10. Critical values of the Hartley statistic for α = 0.05
9.11. Quantiles of the Poisson distribution
9.12. Critical values in Kolmogorov test of goodness-of-fit
9.13. Critical values of a linear correlation coefficient and a partial correlation coefficient
9.14. Critical values of the Spearman’s rank correlation coefficient
9.15. Critical values of a multiple correlation coefficient
9.16a. Critical values Dn,m(α) in the Smirnov test of goodness-of-fit for two empirical distributions
9.16b.Distribution of the Smirnov statistic Dn,m P{Dn,m ≤ k/n}
9.17. Critical values α(2n, 2m) of the distribution
References
Subject index
Biography
Jacek M. Czaplicki (Mining Mechanization Institute, Silesian University of Technology, Gliwice, Poland) has been an academic lecturer for forty years and is continuously associated with his home University. He did, however, leave his school for a couple of years’ lecturing in African universities.
He worked for three years at the School of Mines of the Kwara State College of Technology, Ilorin, Nigeria on a UNESCO project. A few years later, he was appointed to Zambia Consolidated Copper Mines Ltd for three years and worked as a lecturer at the School of Mines of the University of Zambia, Lusaka as part of a World Bank project.
Jacek Czaplicki received a Master of Science in Mine Mechanization from the Silesian University of Technology, Gliwice, Poland. He also obtained a Doctorate degree in Technical Sciences. Later, he submitted a dissertation and passed all of the requirements and was awarded a D.Sc. degree in Mining and Geological Engineering with a specialisation in Mine Machinery at the same home University. Currently, he is a Professor of Mining Engineering.
He has published about a hundred and forty papers and ten books in Poland and abroad. His specialization comprises mine transport, the reliability and computation of mine machinery systems and the reliability of hoist head ropes. In his research, he applies methods and models from mathematical statistics. He is an internationally recognized specialist in mine mechanization.
