What is generally described as the *Stoppa distribution*^{[}^{15}^{]} is the second of five types. Three of the five were also published by others, are better known under different titles and so described elsewhere in this book.

The *Stoppa‐I distribution* is commonly known as the *power distribution*, described later in Section 33.20.

The *Stoppa‐II distribution* is one of three generalisations of the Pareto‐I distribution, defined by adding the shape parameter (*δ*_{2}). Its PDF is

(24.1)

Setting *δ*_{2} to 1 (and *δ*_{1} to *δ*) gives the classic Pareto distribution described by Equation (23.1). Figure 24.1 shows this, as the coloured line, and the effect of increasing it above this value.

The CDF is

(24.2)

Fitting to the NHV disturbance data gives values for *β*, *δ*_{1} and *δ*_{2} are respectively 0, 1.01 and 379. With *RSS* at 0.2108 the fit is an improvement on the standard Pareto distribution but is still poor – as shown by Figure 24.2.

Inverting gives the QF ...

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