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128 Computational Statistics Handbook with MATLAB
end
% Add some whitespace to see better.
axis([-0.5 max(k)+1 min(phik)-1 max(phik)+1])
xlabel('Number of Occurrences - k')
ylabel('\phi (n_k)')
The Poissonness plot has significant curvature indicating that the Poisson
distribution is not a good model for these data. There are also a couple of
points with a frequency of 1 that seem incompatible with the rest of the data.
Thus, if a statistical analysis of these data relies on the Poisson model, then
any results are suspect.
2
1.5
1 1
0.5
0
φ (n k ) −0.5
1
−1
−1.5
−2
−2.5
0 1 2 3 4 5 6 7
Number of Occurrences − k
IG
FI F U URE G 5. RE 5. 1 11 1
F F II GU RE RE 5. 5. 1 1 1
GU
1
This is a basic Poissonness plot using the data in Table 5.1. The symbol 1 indicates that
n k = 1 .
Hoaglin and Tukey [1985] suggest a modified Poissonness plot that is
, which helps account for the variability of the
obtained by changing the n k
individual values. They propose the following change:
⁄
n k – 0.67 – 0.8n k N; n k ≥ 2
⁄
*
n k = 1 e; n k = 1 (5.3)
undefined; n = 0.
k
© 2002 by Chapman & Hall/CRC
