Given is a lognormal distribution with median e and mode <msqrt> e </msqrt> . What is t

rose2904ks

rose2904ks

Answered question

2022-06-21

Given is a lognormal distribution with median e and mode e . What is the variance of the lognormal distribution?
Not sure how to solve this. A variable Y has a lognormal distribution if log ( Y ) has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?

Answer & Explanation

Aaron Everett

Aaron Everett

Beginner2022-06-22Added 18 answers

We know that
1. Mode = e μ σ 2
2. Median = e μ
3. Variance = e 2 μ + σ 2 ( e σ 2 1 )
Using your data you get
{ e μ σ 2 = e 1 2 e μ = e
That means
{ μ σ 2 = 1 2 μ = 1
{ σ 2 = 1 2 μ = 1
Now you can calculate your variance substituting μ and σ in your variance expression finding
V [ Y ] = e 3 ( e 1 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?