Читать книгу Reliability Analysis, Safety Assessment and Optimization - Enrico Zio - Страница 28

A random variable T follows the gamma distribution if and only if the pdf (shown in Figure 1.5) of T is

Figure 1.5 The pdf of the gamma distribution with β=1.99,λ=1_.

(1.33)

where β>0 is the shape parameter and η>0 is the scale parameter of the distribution. The cdf of the gamma distribution is

(1.34)

If T denotes the failure time of an item with gamma distribution, the reliability function will be

(1.35)

The hazard rate function is

(1.36)

The mean, μ, and variance, σ2, are

(1.37)