Data Visualization and Data Summary - Text Mining Techniques for Healthcare Provider Quality Determination - page 40

Figure 6. Kernel density estimate of length of stay for patients with diabetes without modifying the level
of smoothness

provided in Silverman:

ò sf

fxdx ''( )

2

=

- 5

''( ) xdx

2

» 0 212 . s

- 5

However, the procedure can use a different estimator, the simple normal reference (SNR), as the
default for the bivariate estimator:

1

= é
ë

ù

5

s 4

ˆ ê ê ú ú

h

() 3 n

û

along with Silverman's rule of thumb (SROT):

1

-

h = 09 .min[ ˆ,( s Q - Q )/ .] 134 n

5

1 3

and the over-smoothed method (OS):

1

é ù

5

1

ê ê ú ú

h = 3 s

p .

70 n

ë û

Figure 7 increases bwm=10 to increase the level of smoothing. It looks very similar to the graph in
Figure 5. However, it is just a little smoother, and is perhaps a better representation of the population
distribution.