Monte Carlo Integration for Gamma Function in Python - statistics

enter image description hereI need to approximate the gamma function using Monte Carlo Intergration using Python, please help! I am new to this method
Approximate gamma function

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looking for a loss function sensitive to edges for medical image quality enhuncement

For an image-to-image translation task in which I want to generate high-quality images from low-quality images ( MRI Images), I need a loss function to highlight the edges and generate images with sharper edges.
Do you have any recommendation for selecting the desired loss function between Pytorch's loss function??
https://pytorch.org/docs/stable/nn.html#loss-functions
I really appreciate it if anyone can even provide me the code of any predefined loss function for this task.
Thanks
I suppose you are using MSE loss function at the moment? This loss function indeed tends to prefer "smoother" outputs rather than sharp edges.
For image generation tasks, consider using perceptual loss that better correlates with human perception of image quality.
For more details on this loss function see
R. Zhang, P. Isola, A. A. Efros, E. Shechtman, O. Wang The Unreasonable effectiveness of Deep Features as a Perceptual Metric (CVPR 2018).

Lognormal distribution for Monte Carlo Simulation

I have to do this MC Simulation of but the parameters I change should have a lognormal distribution. My problem is that I don't know how to make them have a lognormal distribution. Are the mean and the std deviation found the same way as the normal distribution? Please help me.
Thank you,

Monte Carlo Simulation code/ library in Python

I am trying to learn how to apply Monte Carlo simulation in Python for predicting/estimating time series data such as sales/deposits volumes, interest rates etc. I can understand the basic idea behind the method.
So I am wondering if there is anywhere a practical example of step by step explanation on how to develop the Monte Carlo model (i.e. choose distribution, apply for loop for selected parameters etc.) As you can understand I am new to the 'sport'.
Any help or suggestion/assistance is much appreciated.
Thanks
I looked at Python libraries, such us Statsmodels, but I couldn't find any relevant simulation model. I looked also at examples such as the one below:
Monte Carlo Simulation in Python
but I am searching for something that elaborates more on the application process.

Logistc regression - changes in the deviance

I'm reading about the logistic regression and i came across a phrase that i can't understand. The sentence is as follows (from the book: Introductory Statistics with R, Peter Dalgaard):
"Changes in the deviance caused by a model reduction will be approximately Chi-squared distributed with degrees of freedom equal to the change in the number of parameters"
Could someone explain this phrase to me? To calculate this change i use the Probability density function or the Cumulative distribution function?
Thank you for your time.

sklearn NB classifier: How to get the actual probabilities of individual samples?

I am making a machine learning program which classifies words in one of the following categories: Hardware, Software, None_of_these. I make use of the Multinomial Naive Bayes classifier from sklearn.
The function predict() gives me the prediction of every word, however, I can't see the actual probability (float ranging for 0 to 1.0) that the word matches with the predicted categorie. I didn't find this on sklearn's site either.
Is there a function which gives me the probability of every sample?
Nevermind, I found the solution.:
predict_proba(X) Returns probability estimates for the test vector X.

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