find skewed distribution from probability

I have a parameter z that has the following distribution:

z_distr = [...         
0.9	0.0637	0.1349
0.8	0.0658	0.1298
0.7	0.068	0.1272
0.6	0.0701	0.1247
0.4	0.0723	0.1221
0.2	0.0745	0.1195
0.1	0.0766	0.1144];

with

z_distr(:,1); % probability of finding z between boundaries z_distr(:,2) and z_distr(:,3)

z follows a skewed distribution with the mode of z = 0.09395.

I need to be able to get random values according to the distribution of z.

background: z is a parameter related to the growth rate of an organism. To find inter-individual variability in growth, each individual has a different z value according to the above distribution.

[Jeff Miller]

You need to have more information or make some assumptions to specify the distribution of z so that you can generate random values. For example, your table indicates that 10% of the observations are outside of the range 0.0637--0.1349 but says nothing about what random values should be generated in those 10% of the cases. What are the minimum and maximum scores? Are 5% of scores less than 0.0637 and 5% greater than 0.1349, or is that 10% made up in some other way?

If you can specify an assumed family of this distribution (e.g., lognormal, gamma), then it may be possible to estimate the distribution's parameters from your table and generate random values from that assumed distribution.

Alternatively, if you have the original data values from which this distribution was tabulated, it might be possible to summarize them differently to get an approximate distribution from which to generate.

[bstechel]

So, I have a model which consists of 10 parameters. I have a dataset that is used to calibrate that 10 parameters using a Nelder-Mead optimisation. To find the variation on the parameters i did the following:

I create 1000 Monte-Carlos datasets, that vary from the dataset I have. For al these datasets, i calcuate the best fitting parameter set, and the loss function compared to the original data (goodness of fit value). A survivor function is plotted (left image). It basically gives the boundary loss function for a certain fraction of most fitting Monte-Carlos datasets. Indicated in the image is a 90% confidence (survivor function = 0.1) which corresponds with a loss function of 0.12. So loss functions between 0 and 0.12 contain 90% of the variation.

In the second step, I fix one of the 10 parameters, the z value, on certain values around the optimum (which is 0.09, see right image). Then I optimised the other parameters to fit the data best, and calculate the loss function for each z-value. When I draw a horizontal line on the loss function value of 0.12, corresponding with 0.9% confidence interval, it generate boundaries of z. These are given in the table z_distribution above.

So what i would like to do is to generate random z values according to that distribution.

[Jeff Miller]

Sorry, I don't completely get it. In making the graph on the left, it seems like you generated 1000 "random" z values--one associated with each of the loss function values, so you could randomly select a z from the 900 of them associated with the lowest 900 values of the loss function, if that's what you want. What does the frequency distribution of these 900 z values look like? Is that the distribution you want to sample from?

I don't see the randomness in the graph on the right. Here, it seems like you fixed z values deterministically and then somehow directly computed the loss value associated with each one of them. I suppose you could select z values uniformly between 0.0637--0.1349, but it doesn't seem like you want all the z values to be equally likely.

Sorry I can't be more helpful.