Summation Simplification for Neumerator of Beta Estimator

  • Context: Graduate 
  • Thread starter Thread starter LBJking123
  • Start date Start date
  • Tags Tags
    Beta Summation
Click For Summary
SUMMARY

The discussion focuses on simplifying the equation Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi into the form Ʃ(something - something)yi. The correct simplification is identified as Ʃw_i(x_i - (Ʃ_j x_j w_j)/(Ʃ_k w_k)) y_i, where the term in brackets represents the deviation of x from its mean. The use of separate indices for each summation enhances clarity in the simplification process.

PREREQUISITES
  • Understanding of summation notation and indices
  • Familiarity with weighted averages and means
  • Basic knowledge of algebraic manipulation
  • Experience with statistical estimators, specifically Beta estimators
NEXT STEPS
  • Study the properties of weighted averages in statistics
  • Learn about the Beta estimator and its applications
  • Explore advanced algebraic techniques for simplifying equations
  • Investigate the implications of using different indices in summation
USEFUL FOR

Statisticians, data analysts, and mathematicians involved in statistical modeling and estimation techniques will benefit from this discussion.

LBJking123
Messages
13
Reaction score
0
I need simplify this equation:

Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

Into an equation of the form: Ʃ(something - something)yi

I am pretty sure the first something is xiwi, but I have no idea what the second something would be...

Any help would be greatly appreciated. Thanks!
 
Physics news on Phys.org
LBJking123 said:
I need simplify this equation:

Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

Into an equation of the form: Ʃ(something - something)yi

I am pretty sure the first something is xiwi, but I have no idea what the second something would be...

Any help would be greatly appreciated. Thanks!

Come on, that's easy:
<br /> \sum_i w_i(x_i-\sum_j x_j w_j/\sum_k w_k) y_i<br />
Note that I chose a separate index for each summation for clarity.
The term in brakets is x minus <x>, i.e. the mean of x.
 
Ohhhhh I kept thinking it was going to be

Ʃ(xiwi-(xiwi2)/Ʃwi)yi

I makes more sense when you choose a separate index for each summation.

Thanks for the help DrDu!
 

Similar threads

MHB Finding Method of Moments Estimates for Uniform Distribution Parameters
  • · Replies 2 ·
Replies
2
Views
2K
Graduate $\phi^4$ in $4 - \epsilon$ dimension renormalization beta function
  • · Replies 2 ·
Replies
2
Views
13K
Help with derivation of electric field of a moving charge
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Can a Beta Distribution Model Scores in the Interval [0,1] for Ranked Retrieval?
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Volterra equation of the second kind
  • · Replies 1 ·
Replies
1
Views
927
Graduate Frequency estimation - Minimising the number of samples
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad How to implement proper error estimation using MC
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Technical question about AMO experiment in a paper
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Understand Beta-Binomial Model for Win/Loss Rating Systems
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Calculate velocity of streams impinging at differing angles
  • · Replies 30 ·
2
Replies
30
Views
2K