Transitioning from Discrete to Continuous Distributions in Statistics

Dec 09, 2025

160 likes | 283 Views

This process illustrates the transformation from discrete to continuous probability distributions using histograms. Initially, each bar in the histogram is split into two, continuing until we reach an uncountably large number of infinitely narrow bars. The resulting distribution becomes continuous and uniform between points A and B. Starting with a binomial distribution (p=0.5 and three bars), we note the varying heights of bars; as we split them, the tail-wards bar height decreases more than the center-wards one. Ultimately, we achieve a continuous normal distribution.

abiba

Download Presentation

Transitioning from Discrete to Continuous Distributions in Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

Discrete to Continuous In each step each bar in the histogram is split into two bars.

Now one final step, to an uncountably large number of bars, each infinitely narrow, yielding a continuous, uniform distribution ranging from A to B.

Now I do the same but I start with a binomial distribution with p = .5 and three bars. • Note that the bars are not all of equal height. • Each time I split one, I lower the height of the tail-wards one more than the center-wards one.