BSA Flow Software Installation and User's Guide - CSI

volume is calculated for the class i as
π
∑ 6 1
= j i
j=
cum
Vi
=
V
(see above).
n D
7.10.3 Curve fitting for histograms
i
3
i
× 100 where V is the total equivalent volume of liquid
BSA flow software includes distribution curve fit to help using measurement
results for numerical simulations.
The distribution curve fits P(x)
are calculated from the displayed
histograms meaning that the X and Y scaling modify the curve fit results.
When copying the equation P(x)
from the hisotgram object (see chapter
5.10 Histogram), the equation is the curve fit Probability Density Function
(pdf). For histogram in count, P (x)
has to be multiplied by ∆ x × N
And for histogram in %, P(x) has to be multiplied by ∆x × 100 where
∆x
is the bin width.
Mean and standard
deviation m and s is the mean and the standard deviation and µ and σ are the mean
and the standard deviation of the variable’s logarithm. They are calculated
from the histograms where Ni the number of size classes (bins), ni the
number of particles in each size class and N the total number of particles.
Note that, in case the Probe Volume Correction is applied ni,
is replaced by
cor
the corrected particle number n (refer to chapter 7.11.3)
1
m =
N
1
Ni
∑
i=
1
i i x n
i
s =
1
N
Ni
∑
i=
1
Ni
Ni
µ = ∑ ( ni
ln( x))
σ = ∑ N i=
1
N i=
1
1
( n ( x − m)
i
( n (ln( x)
− µ )
Normal distribution The normal distribution curve fitting can be applied to any type of histogram
data (count, % or pdf). The formula (pdf) is
Log-Normal
1
P(
x)
= e
s 2π
2 2
−(
x−m
) /( 2s
)
distribution The Log-Normal distribution curve fitting can only be applied to size
histograms (count, % or pdf). The formula (pdf) is
Modified Log-Normal
1
P ( x)
= e
xσ
2π
2 2
−(ln(
x)
−µ
) /( 2σ
)
Distribution The Modified Log-Normal distribution curve fitting can only be applied to
size histograms (count, % or pdf). The formula (pdf) is
BSA Flow Software:Reference guide 7-109
i
2
2 )