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A random variable X is said to follow a lognormal distribution if Y = log(X) follows...

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:

110 15 60 5419 15 73 190 57 4344 18 37 43 55 19 23 82 175 50 80 65 63 36 6 10 17 52 43 70 22 95 20 4 17 15 12 29 29 6 22 40 17 26 30 16 116 28 32 33 29 27 16 55 8 2 49 82 85 20 67 27 44 16 6 35 17 26 32 76 150 2 5 6 5 75 23 29 64 22 47 9 10 28 18 84 52 130 50 45 12 2 73
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ReportAnswer #1

A) Please refer following image for Histograms.

Log transformed data have a more normal looking histrogram.

Histogram of Y Histogram of LOGY 50 100 150 200 2 4 Original Values Log Transformed ValuesB) 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

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