Create a Random log normal distribution from given mean and variance of a normal distribution

I have normal distributions with their means and stand deviations and I’m trying to great their lognormal distributions. Although my normal mean and standard deviation are small numbers, their log normal are huge. Is there anything I'm doing wrong and my code are as below. Thank you in advanced.

NormalMean = [14 10.5 3.6 15 12 4.6 3.5 10];

NormaSTD   = [2.1 1.575 0.36 7.5 4.8 1.15 0.875 2]; 

row     = 1000; 
GIP     = zeros(row,length(NormalMean)); 

for i = 1:length(NormalMean)
    
R = lognrnd(NormalMean(i), NormaSTD(i),row,1);

GIP(:,i) = R;

end 

[Torsten]

Where do you define Mean and StandDev ?

[Yaser Khojah]

sorry, i just fixed it.

[Torsten]

Look at how mean and standard deviation of normal and lognormal distribution are connected:

https://de.mathworks.com/help/stats/lognrnd.html

[Yaser Khojah]

Yes, I did, and I have seen this before, but I still did not find an answer for my question.

In the help page, the mean and variance of a log-normal distribution are given and then we calculate the normal distribution parameters, mu and sigma as below b:

μ=log(m2/Gv+m2)

σ=Glog(v/m2+1)

Now I can use Lognrnde as below to create random log-normal numbers as below

X = Lognrnde(mu,sigma)

My question is different, I have the mu and sigma of the a normal distribution and I want to create a log-normal distribution and generate random numbers as well. So, I should be ok to use X = Lognrnde(mu,sigma) directly since I know mu and sigma.

Howvever, when I did that, I got big numbers. I have added my code, if you want to try it. I’m sure there is something is missing.

[Torsten]

If mu and sigma are mean and standard deviation of the normal distribution and you call

X=logrnd(mu,sigma), the lognormal distribution has a mean of exp(mu+sigma^2/2) and a variance of exp(2*mu+sigma^2)*(exp(sigma^2)-1). These are very big numbers in your case.

[Yaser Khojah]

so how would you do mine? is there a way from a given normal distribution, I get a reasonable log random normal distribution numbers?

[Torsten]

If the data given for mu and sigma are those you have to use, you get big numbers from the corresponding lognormal distribution. That's a fact, and it's reasonable.

If the given mu and sigma values are those from the lognormal distribution and not from the underlying normal distribution, it's a different thing.

Answer 1

[Elsa Black]

A random variable X is said to have the lognormal distribution with parameters μ ∈ ℝ and σ > 0 if ln( X) has the normal distribution with mean μ and standard deviation σ. Equivalently, X = e Y where Y is normally distributed with mean μ and standard deviation σ. The lognormal distribution is used to model continuous random quantities like in when the distribution is believed to be skewed, such as certain income and lifetime variables. Distribution 1. Use the change of variables theorem to show that the probability density function of the lognormal distribution with parameters μ and σ is given by f ( x) = 1 √2 π σ x exp(−(ln( x) − μ) 2 2 σ 2 ), x > 0 2. Show that the lognormal distribution is unimodal and skewed right. Specifically, let m = exp( μ − σ 2 ) and show that a. f x is increasing on 0( ), and decreasing on m m ∞( ), , so that the mode occurs at x = m. f ( x) → 0 as x → ∞.b. f ( x) → 0 as x ↓0.

[Yaser Khojah]

Dear Elsa, thank your for your explination. Is there away to check please if I'm doing it right since my resutls are away bigger than the normal mean. Thanks for your time.

[Torsten]

Didn't you read my comment about how mean and standard deviation of the two distributions are connected ?

[Yaser Khojah]

Yes please and check above.