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Random uncertainties

  1. Sep 17, 2010 #1

    In http://sl-proj-bi-specification.web...pecification/Activities/Glossary/techglos.pdf it says that: ... if the sources of uncertainties are numerous, the Gaussian distribution is generally a good approximation.

    I don't quite understand why. The Central Limit Theorem (CLT) only says that if we have a sum S of N random variables, then S will be Gaussian for very large N. So the CLT does not explain the above. In that case, where does the statement come from?

  2. jcsd
  3. Sep 17, 2010 #2


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    The general interpretation is that the effects of those uncertainties are additive - that's where the CLT comes in.
  4. Sep 17, 2010 #3
    But that would only explain why the errors are Gaussian, not why the measured variable is Gaussian.
  5. Sep 17, 2010 #4


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    If the problem is a location problem, the "model" can be described as

    Variable = Mean value + Random error

    with "Mean value" a constant. Since the random error is Gaussian, so is the variable.
  6. Sep 17, 2010 #5
    I am not sure I understand what you mean by "location problem". In my case we are talking about measured speeds.
  7. Sep 17, 2010 #6


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    A "location problem" simply means you are trying to determine the mean value of a variable. A mean is one type of measure of location, or measure of center.

    I don't know exactly what type of problem you're involved in: my posts above were

    1) to show how the Gaussian distribution arises from the "many sources of uncertainty"
    2) to show one way in which a measured random quantity can be assumed to have a gaussian distribution
  8. Sep 17, 2010 #7
    Ok, I understand. In post #2 and #4 you use "error" and "uncertainty" interchangeably. Does

    Variable = Mean value + Uncertainty

    also hold for a location problem?

  9. Sep 17, 2010 #8


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    I guess - the main idea is that the variable is a constant value + some unmeasurable random behavior, which is often modeled by a normal (Gaussian) distribution.

    An approach slightly more general than the location model is given by

    Variable = Model + Error

    where ``Model'' is some deterministic (non-random) expression. Consider multiple regression:

    Y = \underbrace{\beta_0 + \beta_1 x_1 + \dots + \beta_p x_p}_{\text{Model}} + \varepsilon

    with [itex] \varepsilon [/itex] is the random error component
    Last edited: Sep 17, 2010
  10. Sep 17, 2010 #9
    Thanks, it was very kind of you.

    Best wishes,
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