Ieee std 1366-2012 (Revision of ieee std 1366-2003) ieee guide for Electric Power Distribution Reliability Indices

B.6 Log-normal distribution 
The random variable in the Gaussian distribution has a range from -∞ to ∞. In real life, many quantities, 
including distribution reliability, can only be zero or positive. This causes the probability distribution to 
skew, bunching up near the zero value and having a long tail to the right. The degree of skew depends on 
the ratio of mean to standard deviation. When the standard deviation is small compared to the mean, the 
log-normal distribution looks like the Gaussian distribution, as shown in Figure B.3(b). When it is large 
compared to the mean, it does not, as shown in Figure B.3(a). Daily reliability data usually has standard 
deviation values far larger than the mean.
0
0.05
0.1
0.15
0.2
0
4
8
12
16
20
24
28
32
36
40
r
p(
r)
0
0.05
0.1
0
4
8
12
16
20
24
28
32
36
40
r
p(r
)
(a)
(b)
Figure B.3—Log-normal distributions: (a) Mean less than standard deviation 
(b) Mean greater than standard deviation
The usual way of determining if a set of data has a log-normal probability distribution is to take the natural 
logarithm of each value in the data set and examine the histogram. If the histogram looks like a Gaussian 
distribution, then the data has a log-normal distribution. Figure B.4 shows a histogram of the natural logs of 
daily SAIDI data for an anonymous utility. The histogram is approximately normally distributed, so the 
data is approximately log-normally distributed. Roughly a dozen utility data sets have been examined, and 
all are approximately log-normally distributed. No non-log-normally distributed utility data has so far been 
found. In addition, Monte Carlo simulation models of the distribution reliability process produce log-
normally distributed data. Therefore, utility daily reliability is approximately log-normally distributed. 
-20
0
20
40
60
80
100
120
-15
-10
-5
0
5