Abstract
Any kind of empirical determination of probability distributions and their parameters amounts to statistical inference procedures based on samples randomly drawn from a population. The concepts of the statistic and the estimator are introduced, paying attention to their consistency and bias. Sample mean and sample variance are defined, and three most relevant sample distributions are investigated: distribution of sums and differences, distribution of variances, and distribution of variance ratios. Confidence intervals for the sample mean and sample variance are discussed. The problem of outliers is elucidated in the context of robust measures, and linear (Pearson) and non-parametric (Spearman) correlations are presented.
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Širca, S. (2016). Statistical Inference from Samples. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_7
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DOI: https://doi.org/10.1007/978-3-319-31611-6_7
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