E
Esnath
Member
Anyone know how they drew the GEV and GPD distribution graphs for the flood data?
In the April 2014 past paper
In the April 2014 past paper
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Hello
The blue bar charts are frequency graphs.
We start by subdividing the data into blocks of even size, eg 5 years.
Then find the maxima for each block. These are:
128,000, 230,000, 122,000, 84,400, 64,300, 185,000, 85,400, 185,000, 110,000, 92,100, 203,000 and 135,000.
Then we produce a frequency chart:
Flood size Number of block maxima in this range
60-95K 4
95-130K 3
130-165K 1
165-200K 2
200-235K 2
So we have 12 block maxima observation and these are split into bars of height (ratio) 4:3:1:2:2 on the graph.
If we are comparing this frequency distribution chart with a PDF of a distribution, we want the area under the frequency distribution chart to sum to 1. Take the 130K to 165K block where there is a single observation. The area of this block must be 1/12. The width is 35K so the height will be (1/12) divided by 35,000 = 0.00000238. The other blocks will be multiples of this.
The PDF is fitted using MLE with a GEV distribution PDF.
For the other graph, using threshold exceedances, the approach will be similar.
Choose a threshold, eg 100,000.
Look at all the flood levels above 100,000 (can use the ordered data for this).
Work out the exceedance in each case, eg 2000, 2000, 8000, 10,000, 13,000 etc.
Do a frequency table similar to the one above.
Plot the blue graph.
Does this help?
Anna
The blue bar charts are frequency graphs.
We start by subdividing the data into blocks of even size, eg 5 years.
Then find the maxima for each block. These are:
128,000, 230,000, 122,000, 84,400, 64,300, 185,000, 85,400, 185,000, 110,000, 92,100, 203,000 and 135,000.
Then we produce a frequency chart:
Flood size Number of block maxima in this range
60-95K 4
95-130K 3
130-165K 1
165-200K 2
200-235K 2
So we have 12 block maxima observation and these are split into bars of height (ratio) 4:3:1:2:2 on the graph.
If we are comparing this frequency distribution chart with a PDF of a distribution, we want the area under the frequency distribution chart to sum to 1. Take the 130K to 165K block where there is a single observation. The area of this block must be 1/12. The width is 35K so the height will be (1/12) divided by 35,000 = 0.00000238. The other blocks will be multiples of this.
The PDF is fitted using MLE with a GEV distribution PDF.
For the other graph, using threshold exceedances, the approach will be similar.
Choose a threshold, eg 100,000.
Look at all the flood levels above 100,000 (can use the ordered data for this).
Work out the exceedance in each case, eg 2000, 2000, 8000, 10,000, 13,000 etc.
Do a frequency table similar to the one above.
Plot the blue graph.
Does this help?
Anna