Table 4.

Step 3(c) of gammaMAXT

(1) If (i modulo 20 = 1) estimate π,y 0,k and θ:

(a) Set z=0. Create vector v of size S.

(b) Randomly select integer r in [n+1,m].

(c) If T i,r=0, z=z+1, else store T i,r in v.

(d) Repeat steps (b) and (c) until v is full.

(e) Sort v. Remove the 90 % lowest values. The new size of v is $N=\frac{S}{10}$.

(f) Estimate $\pi =\frac{S}{z+S}$.

(g) Estimate y 0 by the minimum of v.

(h) Estimate k: see below.

(i) Estimate $\theta =\frac{1}{\mathit{\text{kN}}}\sum _{i=1}^N\left(v\right[i]-y_0)$.

(2) If (i modulo 20 ≠ 1), use the latest estimated values of π,y 0,k and θ.

(3) Sample M i from the distribution of the maximum, whose CDF is $F_{{\mathcal{Z}}_i}\left(z\right)={\left[\frac{\gamma \left(k,\frac{z-y_0}{\theta }\right)}{\Gamma \left(k\right)}\right]}^{\frac{(m-n)\pi }{10}}$.