Statistical distribution arithmetic
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调研方向
Start with companion issue #1376 and the integration work that must precede this investigation. Explore how distributions, dependence, and arithmetic could be represented, including when well-known distributions can use simplified nodes. Done means establishing whether integral-form processing is feasible for the relevant functions and documenting the resulting approach.
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描述
Companion to #1376. An approximate value (such as a variable with measurement error) should really be interval arithmetic. However, most measurements in life come with a distribution. For example as normal distribution. Interval arithmetic necessarily assumes a uniform distribution by asserting that the variable can be simply described using its minimum and maximum values.
The idea here is to figure out how we can process such distributions. For example, the summation of two normally distributed variables are still normally distributed while the summation of the square of independent standard normal variables distribute as chi-squared. Concepts like dependence also need to be exposed.
Whether we are able to process these distributions in integral form properly for all functions is part of this investigation. Where convenient, a simplified node representing a well known distribution should be used instead. Therefore, this must only start after integration work is done.
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