Question

A random variable X is said to follow a lognormal distribution if Y = log(X) follows a normal distribution. The lognormal is sometimes used as a model for heavy-tailed skewed distributions.

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please answer the follow:

Answer 1

A) Please refer following image for Histograms.

Log transformed data have a more normal looking histrogram.

B) Please refer following image for Normal probability plot.

Log transformed data have a better normal probability plot.

C) Correlation test based on normal probability plot - based on the normal probability plots one caan conclude that LOG(Y) follows a lognormal distribution and correlation between Y and LOG(Y) is quite high.

In this case it is 0.90