Some Handwritten Notes Summarizing Properties of Most Important Probability Distributions (Useful in Statistics and Data Science practice)

Over the past few years of my journey in Statistics and Data Science, I have been repeatedly using some important properties of the most useful probability distributions. Here I am sharing with everyone (yes, it's for You!) my collection of handwritten notes (originally written in a diary) with the wish that it would save tons of time when you are stuck, and going through all resources to find some important properties.This is a PDF file of 23 pages with notes created by me (originally they were in a small diary that i maintained).

Here is the link for the PDF file. I wish someone could hand me over such a collection when i started my journey; as in the hour of need I can just go back and peep into the properties, without being overwhelmed by lots of complicated theories. It's completely FREE for personal use. But if you are interested in commercial use, please let me know. Happy Learning and Happy Sharing!

When would you need this? Say, you are interested in the rth order Moment of the famous Gamma Distribution, or say, Variance of the not-so-famous 2nd kind Beta Distribution. Or maybe you have already implemented Logistic Regression in your dataset(these days packages have made life too easy!), but not sure about the nature of Logistic Distribution (What is the Cumulative Distribution Function, or maybe the mean deviation about mean) .These are useful in day-to-day practices, yet there is no standard collection including most important properties of these 19 distributions(names below) anywhere online available for free (at least i could not find one).

I always searched standard text books or online resources for a chart summarizing these properties, where i can go back again and again when using a specific tool for some data analysis purpose. Such collections exist on a small scale in standard textbooks like Casella Berger(Statistical inference) or Mood Graybill Boes, but they were either incomplete or only trivial properties were given (Though I must admit that I have personally benefitted a lot from these collections, and these books are a great source of knowledge, especially for a strong background in theoretical statistics and data analysis). Thus I started to make my own collection, which grew over the years. This is by no means complete, and I would love to hear back from you for suggestions and improvements. I have worked hard to make the material error-free, still if you find some of the material to be misleading, please let me know.

I have included the following distributions(in this order):

A)Continuous Probability Distributions:

• Rectangular(Uniform)
• Gamma
• Beta (1st and 2nd kind)
• Normal
• Log-Normal
• Cauchy
• Exponential
• Laplace /Double Exponential
• Pareto
• Logistic

B) Discrete Probability Distributions:

• Uniform
• Bernoulli
• Binomial
• Poisson
• Hypergeometric
• Geometric
• Negative Binomial
• Power Series Distributions

Properties included are the Density/Mass Function, CDF, Mean, Median, Mode ,Variance, Mean Deviation, Moment Generating Function/Characteristic Function, the nature of the distribution and its shape(Skewness and Kurtosis), Moments of different orders, and some other properties that I have found useful in practice.

Feel free to refer to any standard textbook(Mentioned Above) or Wikipedia for the proofs , if you are seriously interested in learning and using these properties in a proper context. Happy Learning!