Abstract
In this chapter, the theory of discrete random variables from Chap. 3 is extended to continuous random variables. At first, we give an introduction to the basic definitions and properties of continuous distributions in general. Then we elaborate on the normal distribution and its key role in statistics. Finally, we exposit in detail several other key distributions, such as the exponential and \(\chi ^2\) distributions.
Everybody believes in the exponential law of errors [i.e., the normal distribution]: the experimenters, because they think it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation.
— Poincare Henri,“Calcul Des Probabilités.”
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Härdle, W.K., Okhrin, O., Okhrin, Y. (2017). Univariate Distributions. In: Basic Elements of Computational Statistics. Statistics and Computing. Springer, Cham. https://doi.org/10.1007/978-3-319-55336-8_4
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DOI: https://doi.org/10.1007/978-3-319-55336-8_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55335-1
Online ISBN: 978-3-319-55336-8
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