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I build a few models, each model will produce a normal distribution for the value of a future event. For example, model M1 will produce a normal distribution $n(30, 5^2)$, and the value of the future event observed is 24. Likewise,

M2-> $n(40, 10^2)$, observation: 35

M3-> $n(10, 2^2)$, observation: 20

How do I evaluate the underlying theory used to build M1, M2, M3?

whuber
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Zebra Propulsion Lab
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  • Are all the observations statistically independent? If so, your theory provides a way to collect a set of independent *standardized* observations by dividing the difference between each observation and its predicted value by the standard deviation. That reduces your question to "how can I compare a set of observations to a standard normal distribution," one that is answered in [many threads here](http://stats.stackexchange.com/search?q=fit+normal+distribution+test+goodness). – whuber Dec 24 '13 at 20:11
  • Thanks to @whuber. All observations are independent. I can transform all to standard normal distribution and test the goodness of fit for the observations. – Zebra Propulsion Lab Dec 24 '13 at 23:14
  • The answer by Henry in the duplicate thread lists some of your best options. – whuber Dec 26 '13 at 14:14

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