Randome sampling from a lognormal distribution shape

[#1]

Hi all, 

I have a distribution lognormal with bellow shape/scale parameter (made by 165 data) 

Now I want to randome sampling with different sample size (5pcs, 10pcs...)

What I want is I expect when running more data it will still follow this distribution shape. 
So I want to simulate what kind of data I will receive when sampling 5/ 10/20 samples in different times. 

I expect each time will show abit different result just cause by sampling eror

Are there any way I can do it in Jmp

Justin_Bui_0-1700024289526.png

[#2 · Accepted solution]

If I understand your interest correctly, I think Simulate ( https://www.jmp.com/support/help/en/17.1/#page/jmp/simulate.shtml# ) is what you need.

The idea is so sub-sample from your data and fit Lognormal repeatedly and collect summary statistics. I attach a modified Big Class sample data to illustrate.

Run the script in the data table. It fits Lognormal to "weight" variable, but use "random freq" as Freq.

Now right click on a statistic of interest, and choose "Simulate":

peng_liu_0-1700056256302.png

In the dialog, choose "random freq" on both sides, click Ok:

peng_liu_1-1700056302819.png

And you will get a table like the following:

peng_liu_2-1700056368356.png

The last two columns are the summary statistics of individual fits to sub-samples.

The "random freq" column use "Resample Freq" function:

peng_liu_3-1700059401364.png

What you need to do is to tweak the threshold in the column formula, so you can get the total of 5/10/20 as you wish.

peng_liu_4-1700059480327.png

[#3]

This example illustrates how you can use the parameter estimates for the distribution model to simulate new samples of different sizes.

Names Default to Here( 1 );

// role of arguments
nRows = 25;
nCols = 1;
μ = 1.038356;
σ = 0.7746626;

sample = J( nRows, nCols, Random Lognormal( μ, σ ) );

dt = New Table( "Sample from LogNormal Population",
	New Column( "Sample", "numeric", "Continuous", Values( sample ) )
);

dt << Distribution( Y( :Sample ) );