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ECON
376 |
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Kilkenny |
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Huff's
probability contours |
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PROBi->j = (POPj/Dij)/[SUMj
(POPj/Dij)] |
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=The probability that a person at place i with population
POPi patronizes an establishment in
location j with POPj, that is dij miles away from
place i. Note that this is a ‘proper’
probability (sum to 100% over i).
It also has the main gravity
model feature that the attraction of a place (j) is directly
proportional to its size and inversely proportional to its distance from i. |
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locations |
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A |
B |
C |
D |
E |
j |
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pop |
i |
100 |
80 |
50 |
200 |
75 |
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distances |
A |
2 |
20 |
10 |
30 |
40 |
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B |
20 |
2 |
30 |
50 |
60 |
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C |
10 |
30 |
2 |
40 |
50 |
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D |
30 |
50 |
40 |
2 |
70 |
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E |
40 |
60 |
50 |
70 |
2 |
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sum
over j= |
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POPj/Daj |
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50.00 |
4.00 |
5.00 |
6.67 |
1.88 |
67.54 |
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POPj/Dbj |
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5.00 |
40.00 |
1.67 |
4.00 |
1.25 |
51.92 |
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POPj/Dcj |
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10.00 |
2.67 |
25.00 |
5.00 |
1.50 |
44.17 |
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POPj/Ddj |
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3.33 |
1.60 |
1.25 |
100.00 |
1.07 |
107.25 |
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POPj/Dej |
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2.50 |
1.33 |
1.00 |
2.86 |
37.50 |
45.19 |
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SUM
(POPi) |
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70.83 |
49.60 |
33.92 |
118.52 |
43.20 |
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SUM
(POPj) |
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67.54 |
51.92 |
44.17 |
107.25 |
45.19 |
(transpose of above) |
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check proper probability |
accounts for 100% of the places patronized: |
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PROBaj |
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74% |
6% |
7% |
10% |
3% |
100% |
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PROBbj |
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10% |
77% |
3% |
8% |
2% |
100% |
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PROBcj |
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23% |
6% |
57% |
11% |
3% |
100% |
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PROBdj |
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3% |
1% |
1% |
93% |
1% |
100% |
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PROBej |
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6% |
3% |
2% |
6% |
83% |
100% |
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=> a resident of place A shops in A
74% of the time, shops in B 6% of the time,… |
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