Lognormal Distribution of Labour Force Incomes and Income Disparity

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Discussion Overview

The discussion revolves around the lognormal distribution of annual incomes within a labour force, specifically addressing the proportion of total income earned by the bottom 10% given that the top 10% earns 37% of the total annual incomes. The inquiry touches on theoretical aspects of the lognormal distribution and its implications for income disparity.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant notes the challenge of solving the problem without mean or variance, emphasizing that all necessary information is provided.
  • Another participant asks for clarification on the density of the lognormal distribution and how to rephrase the given information in terms of this density.
  • A participant presents a calculation for the proportion of total income earned by the bottom 10%, suggesting it is 1.28% based on a specific formula involving the cumulative distribution function (CDF).
  • One participant expresses frustration after receiving a negative response from their professor regarding their solution, questioning the correctness of the professor's assessment.
  • Another participant supports the idea of discussing the answer with the professor if others arrive at the same conclusion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the solution provided, with some expressing confidence in their calculations while others question the assessment by the professor. The discussion remains unresolved regarding the accuracy of the proposed solution.

Contextual Notes

The discussion highlights the absence of mean or variance in the problem, which may limit the application of certain statistical methods. There is also a reliance on specific formulas from external sources, which may introduce additional assumptions or dependencies.

mwendazimu
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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 realize that there is no mean or variance!
Also take note that all the information is provided. There is nothing missing in this question,
 
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What is the density of the log normal distribution and how would you rephrase the given information in terms of this density?
 
mwendazimu said:
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 realize 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:
I like Serena said:
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?
 
mwendazimu said:
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.
 

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