rvs

With a couple of changes (logL to logJ, and map made into list) displays the graph:

Assumptions:

1. User is required to enter/select a certain combination of the four 'criteria'
2. Average is taken over scores for which all four of these criteria are satisfied (if fewer, score does not 'qualify' to be 'averaged')

Approach

Each of your criteria can be evaluated in the form of a matrix of 1s & 0s corresponding to 'criteria satisfied' and 'not satisfied' resp. Screenshot refers:

According to Wikipedia, the ppf, or percent-point function (also called the Quantile function), can be written as the inverse function of the cumulative distribution function (cdf), when the cdf increases monotonically.

From the figure shown in the question, the cdf of my custom distribution function does, indeed, increase monotonically - as is expected, since the cdf's of Gaussian and uniform distributions do so too.

The ppf of the general normal distribution can be found in this Wikipedia page under "Quartile function". And the ppf of a uniform function defined between a and b can be calculated simply as p*(b-a)+a, where p is the desired probability.

But the inverse function of the sum of two functions, cannot (in general) be trivially written as a function of the inverses! See this Mathematics Exchange post for more information.

Therefore, the partial "solution" I have found thus far is to save an array containing the cdf of my custom distribution when instantiating an object and then finding the ppf (i.e. the inverse function of the cdf) via 1D interpolation, which only works as long as the cdf is indeed a monotonically increasing function.

NOTE 1: I still haven't fixed the bound's check issue mentioned by Peter O.

NOTE 2: The proposed solution is unviable if an ndarray of loc's were given, because of the lack of a closed-form expression for the Quartile function. Therefore, the original question is still open.

The working code is now:

Here is one approach. You can compute the probability of x being selected under the negative binomial, then normalize the probabilities for xs below max_value to sum to one. Now, you can simply call np.random.choice with appropriate probabilities.

Your issue is not with the integrate function, it is with how the kde function accepts arguments - it only takes one argument (and a class instance argument, which is why it says 2 arguments). So you need to pack your input arguments to kde in a list or a tuple.

To align with how the integrate function passes arguments, you could just make a lambda from kde and apply the integrate function on that, like so

You need to first create the boxes as a reactiveValues object. Then you can control what you display in renderUI. I have shown here for 3 boxes. You can modify it to dynamic number. Try this

I have ported the MATLAB code to estimate Johnson distributions parameters from moments

https://www.mathworks.com/matlabcentral/fileexchange/46123-johnson-curve-toolbox

to Python

https://github.com/maxdevblock/j_johnson_M

Usage

The documentation of root says that, fun is

A vector function to find a root of.

I guess they mean by that the fun is a mapping from nDim -> nDim and not from nDim -> 1.

So one option is two blow up your function artificially to fulfill this requirement.

You can create a custom rv_continuous subclass. The minimum requirement, is that the custom class provides a pdf. The pdf can be obtained from gumbel_l's pdf up till x = 0 and being zero for positive x. The pdf needs to be normalized to get its area equal to 1, for which we can divide by gumbel_l's cdf(0).

With only the pdf implemented, you'll notice that obtaining random variates (.rvs) will be rather slow. Scipy rv_continuous very slow explains this can be remedied by generating too many variates and throwing away the values that are too high, or by providing an implementation for the ppf.

As the ppf can be obtained straightforward from gumbel_l's ppf, the code below implements that solution. A similar approach can be used to truncate at another position, or even to truncate at two spots.