Usually results of direct measurements are normally distrubuted. Also, if we make linear transformation on result. e.g. if X it is a normally distrubuted random variable, also Y=a+bX also it is.

Statement is not any more thrue, if we make exponential or logaritmic transformations. e.g.

if Y has a normal distribution, then Y= exp(X) has a log-normal distribution. (http://en.wikipedia.org/wiki/Lognormal_distribution)

I am interested in the opposite situation. Usually we determine absorbtion by the help of the Beer-Lambert law, measuring intensity of transmitted light.

A=ln(Io/I), where A = absorbtion, Io = the intensity of the incident light, and I= the intensity of transmitted light) I and Io are directly measured, and normally distributed.

My theoretical problem is, what type of distribution has A (the absorbtion)?

More general formulated the question it is: if X has a normal distribution, what type of distribution has Y=lnX?

Thanks for any information. Ican not make further research, because I do not know the name of the distribution (it is not lognormal!!!!!).

Statement is not any more thrue, if we make exponential or logaritmic transformations. e.g.

if Y has a normal distribution, then Y= exp(X) has a log-normal distribution. (http://en.wikipedia.org/wiki/Lognormal_distribution)

I am interested in the opposite situation. Usually we determine absorbtion by the help of the Beer-Lambert law, measuring intensity of transmitted light.

A=ln(Io/I), where A = absorbtion, Io = the intensity of the incident light, and I= the intensity of transmitted light) I and Io are directly measured, and normally distributed.

My theoretical problem is, what type of distribution has A (the absorbtion)?

More general formulated the question it is: if X has a normal distribution, what type of distribution has Y=lnX?

Thanks for any information. Ican not make further research, because I do not know the name of the distribution (it is not lognormal!!!!!).

Last edited: