2.5. Continuous probability distributions

In the continuous case, the range of the random variables under consideration is an interval or a union of intervals.  For a random variable X, defined on the closed interval [a,b],  P(a ≤ X ≤ b) is the probability the outcome of the experiment takes values between a and b. It is obtained by simply  integrating the probability density function f over  the interval [a,b]:  

Below, we discuss the most commonly used continuous probability distributions in seismic hazard analysis.



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.............. 2.5. Continuous probability distributions
.............. 2.5.1. Continuous uniform distribution
.............. 2.5.2. Normal distribution
.............. 2.5.3. Log-Normal distribution
.............. 2.5.4. Exponential distribution

Frank Scherbaum (2015), Fundamental concepts of Probabilistic Seismic Hazard Analysis, Hazard Classroom Contribution No. 001