quantile | Space efficient streaming quantile estimator

I have a table like

Below you will find my python code for a class assignment I was given a couple weeks ago which I have been unable to successfully debug. The problem is about finding the value at risk (i.e., the p% quantile) for an aggregate loss random variable, using FFT. We are given a clear mathematical procedure by which we can gain an estimation of the discretized CDF of the aggregate loss random variable. My results are, however, seriously off and I am making some kind of mistake which I have been unable to find even after hours of debugging my code.

The aggregate loss random variable S is given such that S=sum(X_i for i in range(N)), where N is negative binomially distributed with r=5, beta=.2, and X_i is exponentially distributed with theta=1. The probability generating function for this parametrization is P(z)=[1-\beta(z-1)]^{-r}.

We were asked to approximate the distribution of S by

1. choosing a grid width h and an integer n such that r=2^n is the number of elements to discretize X on,
2. discretizing X and calculating the probabilities of being in equally spaced intervals of width h,
3. applying the FFT to the discretized X,
4. applying the PGF of N to the elements of the Fourier-transformed X,
5. applying the inverse FFT to this vector.

The resulting vector should be an approximation for the probability masses of each such interval for S. I know from previous methods that the 95% VaR ought to be ~4 and the 99.9% VaR ought to be ~10. But my code returns nonsensical results. Generally speaking, my index where the ECDF reaches levels >0.95 is way too late, and even after hours of debugging I have not managed to find where I am going wrong.

I have also asked this question on the math stackexchange, since this question is very much on the intersection of programming and math and I have no idea at this moment whether the issue is on the implementation side of things or whether I am applying the mathematical ideas wrong.

I have a dataset with four variables (a,b,c,d). I want to group the data by a,b,c then find out outliers for d.

Here is the sample data: https://www.dropbox.com/s/ftp4eehqxzh7nn3/example.csv?dl=0

I tried:

I'm trying to use GEKKO to solve quite a large optimization problem locally (with remote=False).

When running the code, I get the error:

I have the dataframe below and I create a kable out of this. How could I add commas between numbers every 3 digits?

With Pandas in Python there is the describe() function that returns the summary statistics for a dataframe. The output is not in a 'tidy' format for simple manipulation with the tidyverse summarise function but it is in a nice format for presentation. My question is how to reproduce this output in R?

I am trying to plot the quantile regression lines for a set of data. I would like to extend the quantile regression lines from geom_quantile() in order to show how they forecast similar to using stat_smooth() with the fullrange argument set to TRUE. However, there is no fullrange argument for geom_quantile(). As an example, see below:

I would like to store the data point label whenever I click it in my plotly plot. The label is the name of the data point that appears in the first column of my data frame.

For example if I hover over a data point it will show me the x and y information as well as the data point name: x: TRUE y: 27 Name: cheeseburger

What I want is to store the label of that data point, 'cheeseburger' as a variable to use later.

I have tried using plotly_click and accessing the event_data but it returns x and y values and all I want is the data point name. This is my code:

I've built this new ggplot2 geom layer I'm calling geom_triangles (see https://github.com/ctesta01/ggtriangles/) that plots isosceles triangles given aesthetics including x, y, z where z is the height of the triangle and the base of the isosceles triangle has midpoint (x,y) on the graph.

What I want is for the geom_triangles() layer to automatically provide legend components for the height and width of the triangles, but I am not sure how to do that.

I understand based on this reference that I may need to adjust the draw_key argument in the ggproto StatTriangles object, but I'm not sure how I would do that and can't seem to find examples online of how to do it. I've been looking at the source code in ggplot2 for the draw_key functions, but I'm not sure how I would introduce multiple legend components (one for each of height and width) in a single draw_key argument in the StatTriangles ggproto.