Calculate and Plot Timing Jitter from Power Spectral Density - python

I have the Power Spectral Density and I need to calculate and plot the Timing Jitter with python. I was surprised that I couldn't find any functions or similar scripts of this online, the only thing I could find was methods for finding the total timing jitter.
Does such a function/method exist?
For reference the data I am trying to plot is example with frequency in the first column and PSD in the second

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How to interpret scipy.stats.probplot results?

I wanted to use scipy.stats.probplot() to perform some gaussianity test on mydata.
from scipy import stats
_,fit=stats.probplot(mydata, dist=stats.norm,plot=ax)
goodness_fit="%.2f" %fit[2]
The documentation says:
Generates a probability plot of sample data against the quantiles of a
specified theoretical distribution (the normal distribution by
default). probplot optionally calculates a best-fit line for the data
and plots the results using Matplotlib or a given plot function.
probplot generates a probability plot, which should not be confused
with a Q-Q or a P-P plot. Statsmodels has more extensive functionality
of this type, see statsmodels.api.ProbPlot.
But if google probability plot, it is a common name for P-P plot, while the documentation says not to confuse the two things.
Now I am confused, what is this function doing?
I looked since hours for an answer to this question, and this can be found in the Scipy/Statsmodel code comments.
In Scipy, comment at https://github.com/scipy/scipy/blob/abdab61d65dda1591f9d742230f0d1459fd7c0fa/scipy/stats/morestats.py#L523 says:
probplot generates a probability plot, which should not be confused with
a Q-Q or a P-P plot. Statsmodels has more extensive functionality of this
type, see statsmodels.api.ProbPlot.
So, now, let's look at Statsmodels, where comment at https://github.com/statsmodels/statsmodels/blob/66fc298c51dc323ce8ab8564b07b1b3797108dad/statsmodels/graphics/gofplots.py#L58 says:
ppplot : Probability-Probability plot
Compares the sample and theoretical probabilities (percentiles).
qqplot : Quantile-Quantile plot
Compares the sample and theoretical quantiles
probplot : Probability plot
Same as a Q-Q plot, however probabilities are shown in the scale of
the theoretical distribution (x-axis) and the y-axis contains
unscaled quantiles of the sample data.
So, difference between QQ plot and Probability plot, in these modules, is related to the scales.
The theoretical probability of an event occurring is an "expected" probability based upon knowledge of the situation. It is the number of favorable outcomes to the number of possible outcomes.
When you gather data from observations during an experiment, you will be calculating an empirical (or experimental) probability.
Example: You tossed a coin and you got a head.
Experimental Probability(head)=1
Theoretical Probability(head)=0.5
For simplicity, see the below diagram which shows probability of getting particular Bill amount. p and q plot are shown.
ppplot (Probability-Probability plot)
Compares the sample and theoretical probabilities (percentiles).
qqplot (Quantile-Quantile plot)
Compares the sample and theoretical quantiles
probplot (Probability plot)
Same as a Q-Q plot, however probabilities are shown in the scale of the theoretical distribution (x-axis) and the y-axis contains unscaled quantiles of the sample data.
Difference between ppplot,qqplot and probplot are related to the scales. Both show sample and theoretical values on x and y axis.
Percentile plots
Percentile plots are the simplest plots. You simply plot the data against their plotting positions. The plotting positions are shown on a linear scale, but the data can be scaled as appropriate.
Quantile plots
Quantile plots are similar to probabilty plots. The main differences is that plotting positions are converted into quantiles or ZZ-scores based on a probability distribution.
The default distribution is the standard-normal distribution. You’ll notice that the shape of the data is straighter on the Q-Q plot than the P-P plot. This is due to the transformation that takes place when converting the plotting positions to a distribution’s quantiles.
Best-fit lines
Adding a best-fit line to a probability plot can provide insight as to whether or not a dataset can be characterized by a distribution.
In statistics and probability quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way.
Probability density of a normal distribution, with quartiles shown. The area below the red curve is the same in the intervals (−∞,Q1), (Q1,Q2), (Q2,Q3), and (Q3,+∞).
In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
If the two distributions being compared are similar, the points in the Q–Q plot will approximately lie on the line y = x. If the distributions are linearly related, the points in the Q–Q plot will approximately lie on a line, but not necessarily on the line y = x.
A Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions.
A P–P plot plots two cumulative distribution functions (cdfs) against each other: It is a probability plot for assessing how closely two data sets agree, which plots the two cumulative distribution functions against each other. P-P plots are vastly used to evaluate the skewness of a distribution.

Plotting the Differential Energy Spectrum from the Energy Spectrum

I have the energy spectrum of a certain number of particles N(E) v/s E.
However, I want to plot the differential energy spectrum i.e. dN/dE v/s E.I DO NOT intend to calculate the derivative here [ as the traditional way of representing a differential energy spectrum might suggest ] What I essentially need is the number of particles in the histogram to be divided by the bin-width.
Is there any way to do this automatically in matplotlib or something similar? Or do I actually need to do this manually, wherein I need to write some code to first put the particles in different bins and then divide by the bin-width and then redraw the histogram.
matplotlib is a graphical library. it can plot data and edit figures.
What you need to do there is apply a numerical method to differentiate your data. It shouldnt be difficult.
You could just apply the definition of the derivative, having as DeltaT the shortest measurement you got of E
Once you got the data you can just use matplotlib to plot it.
if you post the data here i would glady give you an example of how to do it.
or you can just check https://en.wikipedia.org/wiki/Numerical_differentiation

Finding a probability density function that reproduces a histogram in Python

So all the data that I actually have is a picture of a histogram from which I can get heights and bin width, the median and one sigma errors.
The histogram is skewed, so the 16th and 84th quantile are not symmetric. I found that the median and the errors can be replicated with a skewed gaussian function, however the resulting histogram, from my found pdf, is difficult to match no mater how much I play with bin numbers and bin widths.
I understand that I can't possibly recreate the histogram exactly, but I will be very happy with something that is close enough.
My best idea is to loop through possible parameters of the skewed gaussian, make a histogram, somehow quantify the difference (like difference in heights at all points) and find best one. I think that might be a very long process though and I'm very sure there is something in scipy that does this quicker. Please refer me to anything useful if possible.
IMO your best shot is to treat the data as points and fit a function with scipy.optimize.curve_fit
This post might also help:

Draw a histogram of a distribution with a discrete component

I'm performing a simulation of a simple queue using SimPy. One of the questions about the system is what is the distribution of the waiting times by a visitor. What I do is draw a normalized histogram of the sample I get during the simulation process.
This distribution is not purely continuous, we have a non-zero probability of the waiting time being exactly zero, hence the peak near the left end. I want it to be somehow obvious from the picture, what is the actual probability of hitting 0 exactly. Right now the height of the peak does not visualize that properly, the height is even higher than one (the reason is that many points are hitting a small segment near zero).
So the question is the general visualization technique of such distributions that are mixtures of a continuous and a discrete one.
(based on the discussion in the comments to OP).
For a distribution of some variable, call it t, being a mixture of a discrete and and continuous components, I'd write the pdf a sum of a set of delta-peaks and a continuous part,
p(t) = \sum_{a} p_a \delta(t-t_a) + f(t)
where a enumerates the discrete values t_a and p_a are probabilities of t_a, and f(t) is the pdf for the continuous part of the distribution, so that f(t)dt is the probability for t to belong to [t,t+dt).
Notice that the whole thing is normalized, \int p(t) =1 where the integral is over the approprite range of t.
Now, for visualizing this, I'd separate the discrete components, and plot them as discrete values (either as narrow bins or as points with droplines etc). Then for the rest, I'd use the histogram where you know the correct normalization from the equation above: the area under the histogram should sum up to 1-\sum_a p_a.
I'm not claiming this being the way, it's just what I'd do.

How to use interpolation to calculate a force based on angle

I am trying to make a python script that will output a force based on a measured angle. The inputs are time, the curve and the angle, but I am having trouble using interpolation to fit the force to the curve. I looked at scipy.interpolate, but I'm not sure it will help me because the points aren't evenly spaced.
numpy.interp does not require your points to be evenly distributed. I'm not certain if you mean by "The inputs are time, the curve and the angle" that you have three independent variables, if so you will have to adapt it quite a bit... But for one-variable problems, interp is the way to go.

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