Best visualization of joint/marginal distributions?

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SUMMARY

The discussion focuses on effective visualizations for joint and marginal distributions, specifically for the functions ƒx(x), ƒy(y), ƒ(X|Y=y), and ƒ(Y|X=x). The user seeks to improve their understanding of these concepts as they prepare for actuary exams. They express familiarity with integration and mathematical concepts but struggle with visualizing distributions accurately. The conversation emphasizes the importance of clear visual representations to identify limits in statistical distributions.

PREREQUISITES
  • Understanding of joint and marginal distributions in statistics
  • Familiarity with conditional probability functions
  • Basic knowledge of statistical visualization techniques
  • Experience with integration and multivariate calculus
NEXT STEPS
  • Research effective visualization techniques for joint distributions using tools like R or Python's Matplotlib
  • Explore the use of contour plots and heatmaps for visualizing marginal distributions
  • Learn about the application of kernel density estimation for better understanding of distributions
  • Study the use of ggplot2 in R for creating advanced statistical graphics
USEFUL FOR

This discussion is beneficial for actuaries, statisticians, data scientists, and students preparing for exams who seek to enhance their understanding of statistical distributions and their visual representations.

nycixc
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I'm trying to get a better visualization of joint/marginal distributions. It's my weakest conceptual area as I pursue the actuary exams, and I want to fully understand this on a more statistical level.

I've taken linear/diff-eq/multivariate, so I'm completely comfortable with the integration and other menial work involved, but I feel like I am lacking in the area of visualizing the distribution, and therefore am incorrectly identifying the limits needed. I'm used to looking at a shape and identifying the limits that way or being given the limits flat-out.

So for ƒ(x,y), what are the best visualizations you've got for:
ƒx(x), ƒy(y), ƒ(X|Y=y), and ƒ(Y|X=x), given 0 < x < y < 1 or x>0, y>0.(I've seen the marginals represented using Σp(x,y), but anything will help!)
 
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