Poisson probability Formula

The Poisson probability formula uses an expected number of mishaps based upon previous experience (Hays 1988,144-45). 

The next step is to plug the values into the formula. In the Poisson probability equation, the term e is the base of a natural logarithm, which is approximately equal to 2.718, and the variable X represents the specific number of defective units being investigated. In this example, X = 3. Therefore, we have ... 

The first step is to implement a Poisson model characterized by a mean with one interindividual variance term (see Model 1 in the appendix). The estimate of the population X was approximately 1.42 episodes per day with a 74% interindividual coefficient of variability (CV). Although not executed in the original analyses, for comparison purposes, a zero-inflated Poisson model was also evaluated (Model 2 in the appendix). The estimated probability of the nonsusceptible state was 0.342 (71% interindividual CV). The ZIP population X estimate was 2.33 (55% interindividual CV) episodes per day. Using the formulas given in Eq. (27.11) and (27.12), the population expectation (variance) was 1.53 (2.76) episodes per day. Note the overdispersion as indicated by the variance greater than the expected value. Figure 27.4 shows the predicted probability from the Poisson and the ZIP... 

The above expression is obtained by best fit of known Pi 0>0i) pairs. These pairs correspond to 2, 10 and 50 percent in 50 years earthquakes that have known probabilities of exceedance Pi. The corresponding maximum interstorey drift limit values 0i, for these three earthquakes, are obtained using the pushover analysis. According to Poisson s law the annual probability of exceedance of an earthquake with a probability of exceedance p int years is given by the formula ... 

Fortunately statistical theory provides the necessary tools. Statisticians usually claim that accident occurrence is explained by the Poisson distribution. The probability that a railroad will have x adverse safety occurrences in a given year is given by the formula ... 

Correspondingly, the probability AP(f(f) to form no nuclei within Au can be expressed by means of the Poisson formula (see Chapter 3, equation (3.1)) ... 

---