I want to model battery lifetime, which decrements continuously at every epoch (i.e., work-cycle) in the following way. So it takes values such as 100, 99.7, 99.3, 99.2, ... 0 (a continuous random variable). How can I convert it into Gaussian distribution? Also, how to normalize the resultant Gaussian distribution with an arbitrary mean and standard deviation?
My apologies if question is not correct as I am new to the probabilistic modeling.
You probably want to model the battery depletion per unit time as Gaussian. So if the battery charge measured each minute is
100, 99.7, 99.3, 99.2, ...
then I'd take the differences between successive values
0.3, 0.4, 0.1, ...
and fit something to that. Now it's probably better to graph the data first and decide if a Gaussian model appears to be valid, but let's say you've done that.
A Gaussian distribution is determined completely by its mean and variance, and the usual ways of fitting the model generally reduce to calculating your sample mean and variance and taking the Gaussian distribution with those parameters. If you normalize this, you'll get the mean-0 variance-1 Gaussian no matter what your input data was.