I know that a standard normal distribution has mean 0, sd=1, skewness=0, and kurtosis=0. I can then transform a value and calculate which percentile it sits. 1.96 is in the top 97.5%
Can I perform a similar calculation when the skewness and kurtosis imply the distribution is not normal? ie. skewness=-2.2, kurtosis=3.1
If I were to deal with this data set, should I perform a transformation to try and make it normal, as I would like to predict where a value would fall in an almost normal distribution (ie with mean=0, sd=1, skewness=-2.2, and kurtosis = 3.1).
In short, I have a value of 1.96, will this fall in top 97.5% of the data? Given a value, can I predict where it would sit in the distribution?
Everything I read online explains how to calculate skewness and kurtosis but not find a way of predicting where a value would sit given these factors to consider as well