Understanding PDF Definition in Stat Theory | Question on Divisor & Histogram

  • Context: Graduate 
  • Thread starter Thread starter member 428835
  • Start date Start date
  • Tags Tags
    Theory
Click For Summary
SUMMARY

The probability density function (pdf) is defined as \lim_{\substack{N\to \infty\\ \Delta c \to 0}}\frac{H(c,\Delta c,N)}{\Delta c}, where H represents a histogram, \Delta c is the bin width, and N is the number of observations. The division by \Delta c ensures that the integral of the pdf equals 1, which is a fundamental property of probability distributions. This definition is crucial for accurately representing continuous random variables and their distributions.

PREREQUISITES
  • Understanding of probability density functions (pdf)
  • Familiarity with histograms and their construction
  • Knowledge of limits in calculus
  • Basic concepts of statistical theory
NEXT STEPS
  • Study the properties of probability density functions in detail
  • Learn about the relationship between histograms and pdfs
  • Explore the concept of limits in calculus, particularly in statistical contexts
  • Investigate the implications of the integral of a pdf equaling 1
USEFUL FOR

Statisticians, data analysts, and students of statistics seeking to deepen their understanding of probability density functions and their mathematical foundations.

member 428835
hey pf!

can someone help me understand why a pdf is defined in the following manner: [tex]\lim_{\substack{N\to \infty\\ \Delta c \to 0}}\frac{H(c,\Delta c,N)}{\Delta c}[/tex] where [itex]\Delta c[/itex] is the width, [itex]N[/itex] is the observation number? Specifically, why the divisor? why is this necessary? [itex]H[/itex] is a histogram.

any insight is greatly appreciated!

thanks!
 
Last edited by a moderator:
Physics news on Phys.org
I'm not familiar with your notation. However, in general, the integral of a pdf must be 1, so I presume the division is to insure that this holds.
 
sorry, i was worried about being too vague, but i think youre right.
 

Similar threads

MHB Axioms of Set Theory .... and the Union of Two Sets ....
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Orthogonality of variations in Faddev-Popov method for path integral
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Definitions of the Riemann integral
  • · Replies 14 ·
Replies
14
Views
3K
MHB Understanding a problem in ring theory
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Hard-Core Boson Model in K space
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Understanding how to derive the differential cross-section formula
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Understanding Goldstone's Theorem Proof: Volume Limit and Commutator
  • · Replies 1 ·
Replies
1
Views
2K
Theory question about neutrals in circuits
  • · Replies 32 ·
2
Replies
32
Views
4K
Graduate On the relationship between Chern number and zeros of a section
  • · Replies 3 ·
Replies
3
Views
4K