Lognormal distribution

  • Thread starter mwendazimu
  • Start date
  • #1

Main Question or Discussion Point

A labour force's annual incomes are lognormally distributed. If the labour force is arranged in order of decreasing annual incomes and the top 10% earns 37% of the total annual incomes, what proportion of the total annual income does the bottom 10% earn?


Kindly help on this one. It looks simple until you start solving and you realise that there is no mean or variance!
Also take note that all the information is provided. There is nothing missing in this question,
 

Answers and Replies

  • #2
Welcome to PF

What is the density of the log normal distribution and how would you rephrase the given information in terms of this density?
 
  • #3
I like Serena
Homework Helper
6,553
176
A labour force's annual incomes are lognormally distributed. If the labour force is arranged in order of decreasing annual incomes and the top 10% earns 37% of the total annual incomes, what proportion of the total annual income does the bottom 10% earn?


Kindly help on this one. It looks simple until you start solving and you realise that there is no mean or variance!
Also take note that all the information is provided. There is nothing missing in this question,
proportion bottom 10% = [TEX]1 - \Phi ( \Phi^{-1}(0.9) + \Phi^{-1}(0.37) - \Phi^{-1}(0.1) )[/TEX] = 1.28%
 
Last edited:
  • #4
proportion bottom 10% = [TEX]1 - \Phi ( \Phi^{-1}(0.9) + \Phi^{-1}(0.37) - \Phi^{-1}(0.1) )[/TEX] = 1.28%
I gave the exact solution and was given a big X. Could my professor be wrong?
 
  • #5
I like Serena
Homework Helper
6,553
176
I gave the exact solution and was given a big X. Could my professor be wrong?
What I gave is my 2 cents, which I derived using the formulas given on wikipedia.
If you came out to the same answer that should be enough reason to go talk to your professor I guess.
 

Related Threads for: Lognormal distribution

  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
1
Views
6K
Replies
6
Views
7K
Replies
3
Views
11K
Replies
12
Views
660
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
3K
Replies
0
Views
2K
Top