In the reliability analysis of hydrosystems engineering problems, several probability distributions are used frequently. Based on the nature of the random variable, probability distributions are classified into discrete and continuous types. In this section, two discrete distributions, namely, the binomial distribution and the Poisson distribution, that are used commonly in hydrosystems reliability analysis, are described. Section 2.6 describes several frequently used univariate continuous distributions. For the distributions discussed in this chapter and others not included herein, their relationships are shown in Fig. 2.15.
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Figure 2.15 Relationships among univariate distributions. (After Leemis, 1986.) |
Computations of probability and quantiles for the great majority of the distribution functions described in Secs. 2.5 and 2.6 are available in Microsoft Excel.
