# Error bars for unknown distribution

#### gmeroni

##### New Member
I recently made a graph where I show the error bars for a certain number of "experiment". In another way, in my algorithm I'm minimizing the objective function so I would expect that increasing the sampling I'll get lower value of the objective function.

As you can see in the graph, the second value from the left, 2.5 on the x-axis, contain only 2.5% of the configurations, so we wouldn't expect it to perform as well as if we used 100% of the configurations.

I think that this is related to the **asymmetry** of the distributions. Is there any approach that can fix this problem - aka a method to compute CI for asymmetric unknown distributions?

This example should be useful to make this graph understandable!

i = number of replicates (with different seed so different sampling every replicate)
z = objective function value
n = number of configurations
j = 1...n

Example: n=1000, i=100

1. Step 1. Analyze all the 1000 configurations and compute the minimum
of z_j. Store it and replicate for i. Then compute mu and sigma of
those z_i
2. Step 2. Analyze 50% of the initial 1000 configuration and
compute the minimum of z_j. Store it and replicate for i. Then
compute mu and sigma of those z_i
3. Step 3. Analyze 10% of the initial 1000
4. Step 4. Analyze 5% of the initial 1000
5. Step 5. Analyze 2.5% of the initial 1000

So we will have mu_100, mu_50, mu_10, mu_5, mu_2.5 and mu_1 and sigma_100, sigma_50,...
Now I'm able to make those error bars like mu_100 + - 2 * sigma_100....