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Math Help - Applications in Discrete Distributions

  1. #1
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    Applications in Discrete Distributions

    Hello,

    New Year Greetings!

    Could anyone please help me.I am given that one way in which the incidence pattern can change is that the incidence rate rise from 0.0001 per month in a population of 30000 to 0.00015 for a six month period and then return to its previous rate ( 0.0001 ) .If the number of occurences in at least 3 out of six month is 5 or more then event H is reported.How could I find the probabilty that the event H is wrongly reported over a particular six month period .

    Kind Regards,

    siddharth
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sidhu View Post
    Hello,

    New Year Greetings!

    Could anyone please help me.I am given that one way in which the incidence pattern can change is that the incidence rate rise from 0.0001 per month in a population of 30000 to 0.00015 for a six month period and then return to its previous rate ( 0.0001 ) .If the number of occurences in at least 3 out of six month is 5 or more then event H is reported.How could I find the probabilty that the event H is wrongly reported over a particular six month period .

    Kind Regards,

    siddharth
    Assume that in a period of 6 months that the incidence is either 0.0001 or 0.00015 and does not change during the six months.

    The number occurrences in each case is (approximately) a Poisson random variable with expected numbers of occurrences of 3 and 4.5 respectively per month.

    For wrongly reporting H we assume that the true expected number of occurrences per month is 3 and use the Poisson distribution to calculate the probability p(5+) that in any given month 5 or more occurrences are reported.

    Now the number of months in our six month window for which 5 or more occurrences are reported is a Binomially distributed random variable ~B(6,p(5+)). So the probability of wrongly reporting H is:

    P = b(3;6,p(5+)) + b(4;6,p(5+)) + b(5;6,p(5+)) + b(6;6,p(5+))

    CB
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  3. #3
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    Poisson Distribution Applications

    Could you please tell if I am right :

    P(the incidence H is reported sometime in 6 months ) =1- P( it is wrongly reported in all 6 months ) = 1 - P( X > =5 when mean is 3 ).

    If the incidence H occurs for 6 months , then what the probability should be that the incidence H is reported by the end of 6 month period ?

    Kind Regards,
    siddharth

    Quote Originally Posted by CaptainBlack View Post
    Assume that in a period of 6 months that the incidence is either 0.0001 or 0.00015 and does not change during the six months.

    The number occurrences in each case is (approximately) a Poisson random variable with expected numbers of occurrences of 3 and 4.5 respectively per month.

    For wrongly reporting H we assume that the true expected number of occurrences per month is 3 and use the Poisson distribution to calculate the probability p(5+) that in any given month 5 or more occurrences are reported.

    Now the number of months in our six month window for which 5 or more occurrences are reported is a Binomially distributed random variable ~B(6,p(5+)). So the probability of wrongly reporting H is:

    P = b(3;6,p(5+)) + b(4;6,p(5+)) + b(5;6,p(5+)) + b(6;6,p(5+))

    CB
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Sidhu View Post
    Could you please tell if I am right :

    P(the incidence H is reported sometime in 6 months ) =1- P( it is wrongly reported in all 6 months ) = 1 - P( X > =5 when mean is 3 ).

    If the incidence H occurs for 6 months , then what the probability should be that the incidence H is reported by the end of 6 month period ?

    Kind Regards,
    siddharth
    I'm not sure what you mean here. It does not look like you are asking a question that is directly related to the original.

    CB
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  5. #5
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    Poisson Distribution Applications

    Hello ,

    There is one additional event other than incidence H ( rate = 0.00015 ) which could change the given incidence rate ( 0.0001 ).This is the incidence M which is reported if the number of occurences in one month is > = 8.

    If the incidence rate is at its actual rate ( 0.0001 ) , is it possible to find the probabilty that the incidence M is wrongly reported sometime in a 6 month period.Also, if the incidence M occurs at the start of a 6 month period after which the rate returns to the original (0.0001), what should be the probabilty that event M is reported in the 6 month period .


    Kind Regards,

    siddharth
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  6. #6
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    The rate of second incidence M is 0.0003 when population is 30,000

    Kind Regards,

    siddharth



    Quote Originally Posted by CaptainBlack View Post
    I'm not sure what you mean here. It does not look like you are asking a question that is directly related to the original.

    CB
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