Abstract
As mentioned at the beginning of Chapter 3, the two important types of random variables are discrete and continuous. In this chapter, we study the second general type of random variable that arises in many applied problems. Sections 4.1 and 4.2 present the basic definitions and properties of continuous random variables, their probability distributions, and their moment generating functions. In Section 4.3, we study in detail the normal random variable and distribution, unquestionably the most important and useful in probability and statistics. Sections 4.4 and 4.5 discuss some other continuous distributions that are often used in applied work. In Section 4.6, we introduce a method for assessing whether given sample data is consistent with a specified distribution. Section 4.7 discusses methods for finding the distribution of a transformed random variable.
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Notes
- 1.
MINITAB, R and other statistical packages calculate F(x; α, β) once values of x, α, and β are specified.
Bibliography
Bury, Karl, Statistical Distributions in Engineering, Cambridge University Press, Cambridge, England, 1999. A readable and informative survey of distributions and their properties.
Johnson, Norman, Samuel Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vols. 1–2, Wiley, New York, 1994. These two volumes together present an exhaustive survey of various continuous distributions.
Nelson, Wayne, Applied Life Data Analysis, Wiley, New York, 1982. Gives a comprehensive discussion of distributions and methods that are used in the analysis of lifetime data.
Olkin, Ingram, Cyrus Derman, and Leon Gleser, Probability Models and Applications (2nd ed.), Macmillan, New York, 1994. Good coverage of general properties and specific distributions.
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Devore, J.L., Berk, K.N. (2012). Continuous Random Variables and Probability Distributions. In: Modern Mathematical Statistics with Applications. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0391-3_4
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DOI: https://doi.org/10.1007/978-1-4614-0391-3_4
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