+ Reply to Thread
Results 1 to 5 of 5

Thread: probability function of sum of multiple normal distributions

  1. #1
    Points: 129, Level: 2
    Level completed: 58%, Points required for next Level: 21

    Posts
    2
    Thanks
    0
    Thanked 0 Times in 0 Posts

    probability function of sum of multiple normal distributions




    I have four normally distributed random variables which may/may not be correlated. I want to find the probability distribution function of the sum? For example, if means were 10,15,20,10 and sd=4,2,3,5 respectively - what would the probability the sum of the variables would be greater than lets say 70?

    I am trying to do this in R. Would this be just the sum of the means and square root of the sum of the variance as the SD and draw from that distribution? Or is there something I am missing....any help would be appreciated!

    Thanks!

  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Posts
    3,020
    Thanks
    12
    Thanked 565 Times in 537 Posts

    Re: probability function of sum of multiple normal distributions

    The sum will follow a normal distribution if they are jointly follow a multivariate normal.

    Your calculation is correct if they are uncorrelated.

  3. #3
    Devorador de queso
    Points: 95,940, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,937
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: probability function of sum of multiple normal distributions

    That is a big "if" though. If they are correlated it will still follow a normal distribution with that same mean but the standard deviation will be different.
    I don't have emotions and sometimes that makes me very sad.

  4. #4
    Omega Contributor
    Points: 38,413, Level: 100
    Level completed: 0%, Points required for next Level: 0
    hlsmith's Avatar
    Location
    Not Ames, IA
    Posts
    7,004
    Thanks
    398
    Thanked 1,186 Times in 1,147 Posts

    Re: probability function of sum of multiple normal distributions

    Quote Originally Posted by Sf26 View Post
    I have four normally distributed random variables which may/may not be correlated.
    Or do you have parameters for these four variables? I am guessing you don't have the actual data, right?
    Stop cowardice, ban guns!

  5. #5
    Points: 129, Level: 2
    Level completed: 58%, Points required for next Level: 21

    Posts
    2
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: probability function of sum of multiple normal distributions


    Quote Originally Posted by Dason View Post
    That is a big "if" though. If they are correlated it will still follow a normal distribution with that same mean but the standard deviation will be different.

    I do have the actual data with sample means and deviations. I was concerned that if you had two normal distributions - one has a peak of lets say 50 another has a peak of 5 , are you able to draw from that distribution as normal even though the combination are two separate "humps"?

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats