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Math Help - Lognormal distribution

  1. #1
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    Lognormal distribution

    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,
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  2. #2
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    Quote Originally Posted by fungus View Post
    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,
    "the top 10% earns 37% of the total annual incomes" lets you write down an equation involving mean and sd, but that's one equation and two things unknown. So you do need another bit of information .....
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  3. #3
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    hmmmm

    The question is complete. You need to work it from first principles. can you derive the mean of a lognormal distribution using
    E(x)= integrate(0 to infinity) X . f(x) dx
    If you can do that you can handle the question.
    Try this technique and you will surely give me the answer.
    Please do not attempt the MGF technique because it will give you the mean but it cannot guide you in answering the question.
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