In simple terms: a lognormal distribution is the result of a function that produces output data.
Following below is the equation and explanations. | ||||
Important property of this distribution is that it does not take values less than 0. But how do we get this shape? A lognormal distribution is very much what the name suggest "lognormal". I explain this as follows: Imagine that you have a function that is the exponent of some input variable. The input variable itself is a normal distribution function. |
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e.g. $$ y = k.e^r $$
Now, if we take a natural log of this function then we end up with a normal distribution. Why? because taking a natural log on an exponent function returns you the input variable and we have already stated that the input variable is a normal distribution. |
Variables |
Stock(10) = stock. |
Interest rate(0.08)= Interest rates( Mean %): |
Volatility(0.4) = Volatility(%) |
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