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The Lognormal Distribution
If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable.
If P1, P2, P3, ... are the prices of a scrip in periods 1, 2, 3, ..., some applications in finance require ln (P2/P1), ln (P3/P2),... to be normally distributed, that is, continuously compounded returns are required to be normal. This property is described as “Stock Prices are Lognormal”.
REMARK
The previous random variables arose out of natural experiments. The following distributions are derived distributions. That is, it is a function of other distributions. We require the following two distributions in Testing of Hypothesis. and our presentation will be restricted by our requirements.
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Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
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