What exactly is a general probability distribution?

Click For Summary
SUMMARY

A "general probability distribution" refers to a probability function that encompasses a broad range of distributions without being limited to specific types. It implies that the concepts and related work discussed can be applied universally across all probability distributions. In mathematical terms, a general probability distribution can be defined as a function F(x) that is increasing, with limits where F approaches 0 as x approaches negative infinity and F approaches 1 as x approaches positive infinity. This definition clarifies the use of "general" in the context of probability distributions.

PREREQUISITES
  • Understanding of basic probability theory
  • Familiarity with mathematical functions and limits
  • Knowledge of statistical mechanics concepts
  • Ability to interpret mathematical notation
NEXT STEPS
  • Research the properties of cumulative distribution functions (CDFs)
  • Explore different types of probability distributions, such as normal and binomial distributions
  • Learn about the applications of general probability distributions in statistical mechanics
  • Study the concept of convergence in probability theory
USEFUL FOR

Students of statistics, researchers in statistical mechanics, and anyone seeking to deepen their understanding of probability distributions and their applications.

Zacarias Nason
Messages
67
Reaction score
4
I'm watching a Stat. Mech. lecture and in it, the lecturer mentions a "general probability distribution" but doesn't explain what exactly that is, yet in the context of the video, everything necessary to understand is understood.

On some cursory google searches I'm finding several hits for a "general probability distribution" in papers and abstracts, but I am struggling to find a good definition. What is a good way to define this? Obviously the word "general" wasn't just thrown in there to confuse people, what does this mean? Does "for a general probability distribution" literally just mean that any of the related work/concepts is applicable to all probability distributions?
 
Physics news on Phys.org
Zacarias Nason said:
Does "for a general probability distribution" literally just mean that any of the related work/concepts is applicable to all probability distributions?

That's the way I would interpret it. Perhaps the author should have said for a "given" probability function.
 
  • Like
Likes   Reactions: Zacarias Nason
I would take it to mean, in one dimension, a function F(x), such that F is increasing, the limit, as x goes to negative infinity, is 0, and the limit, as x goes to infinity, is 1.
 
  • Like
Likes   Reactions: Zacarias Nason

Similar threads

Undergrad Radiant Intensity from Radiant Power and Intensity Distribution
  • · Replies 17 ·
Replies
17
Views
5K
Undergrad The Probability Distribution and 'Elements of Reality'
  • · Replies 109 ·
4
Replies
109
Views
7K
Undergrad Does the generalized gamma distribution have a mgf?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What Is the Probability Atom A Will Emit a Photon Before Atom B?
  • · Replies 4 ·
Replies
4
Views
2K
Most probable velocity from Maxwell-Boltzmann distribution
  • · Replies 5 ·
Replies
5
Views
747
Graduate Maxwell distributions and average, RMS, and most probable speeds
  • · Replies 3 ·
Replies
3
Views
3K
Neutron's crow flight distance & 2° moment of a distribution
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Stat Mech, question about average of function of ith state.
  • · Replies 1 ·
Replies
1
Views
1K
Graduate On the width of the kinetic energy distribution of a gas
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
4K