I am trying to understand how to correctly use the lognormal distribution. Let's say I have a list of Adjusted Price of a stock, I know that its daily returns is normally distributed, and because stock prices are positive numbers, it would be better to use a lognormal distribution. However, how should I interpret the lognormal distribution? I have 2 interpretations in mind:

ONE All the (historical) Adjusted Prices can fit into a lognormal distribution, and using this PDF, I can find the probability of a range of prices.

TWO Using the mean and standard deviation of Adjusted Prices, I can plot a lognormal distribution of a given price, and predict the probabilities of the predicted stock price?

Which one is the correct interpretation? If both are wrong, what will be the correct way of me interpreting and using lognormal distribution?


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