I want to apply a filter to my data that assume its normality. The data comes from different sensors measuring the same quantity over the same period of time.
Using a simple histogram plot, It seems that the data of most of the sensors follows a lognormal distribution, so my idea was to apply the following process:
- fit a lognormal distribution to the data to estimate the shift of the distribution (as I asked in a previous post).
- shift the data according to the estimated parameter, and apply the logarithm to transform the data to normal
- apply the filter to data that should now better follow a normal distribution.
What I would like to do is:
- to have a way to quantify and compare the "improvement" of normality of the data before and after the transformation, to see if the transformation is significant (at least in some cases).
- test for log-normality of the data to see whether to apply this transformation (could I transform and test for normality?).
- test for log-normality at different time aggregations/time intervals and compare them
Looking to a previous question, I identified three different statistical tests, but I'm not sure whether these can be meaningfully applied to my case, and used for making these kinds of comparisons:
- Kolmogorov–Smirnov test
- Lilliefors test (normality testing without assuming distribution parameters)
- Akaike information criterion
