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- Thread starter SamanthaYellow
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In summary: The error propagation rule is based on the assumption that the errors are Gaussian distributed. But since the distribution of the errors is not Gaussian, the error propagation rule does not work.

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Simplify writing by assuming means are 0. E((X+Y)²)=E(X²)+2E(XY)+E(Y²). IF X and Y are independent (uncorrelated is enough), E(XY)=E(X)E(Y)=0.

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Not necessarily. E((XY)^2)=E(X^2)E(Y^2), so you have variances multiplying, not adding.

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The higher order terms depend not only on the statistics of x but also on the Taylor series. It might be that they all disappear for a Gaussian, as higher order correlation functions can all be expressed in terms of ##E(x^2)##.

You say that your error is lognormal distributed?

So why don't you use error propagation for the logarithmized independent variable , i.e. replacing Var(f(y) by ##Var(f(e^x))##?

Error propagation for non-normal errors is a statistical method used to estimate the uncertainty or error in a numerical result when the underlying data does not follow a normal distribution. This method takes into account the non-normality of the data and provides a more accurate estimation of the error compared to traditional methods that assume normality.

Error propagation is important for non-normal errors because it allows for a more accurate and reliable estimation of the uncertainty in a numerical result. When the underlying data is not normally distributed, traditional methods may underestimate or overestimate the error, leading to incorrect conclusions or decisions based on the results.

Error propagation for non-normal errors takes into account the non-normality of the data, while traditional error propagation assumes that the data follows a normal distribution. This means that the calculations and assumptions used in non-normal error propagation are different from those used in traditional methods.

Some common non-normal distributions that require error propagation include Poisson, exponential, and log-normal distributions. These distributions are commonly encountered in scientific and engineering data, and their non-normality can greatly affect the accuracy of error estimation.

Yes, error propagation can be applied to any type of non-normal distribution as long as the distribution is known or can be estimated accurately. However, the specific method and assumptions used for error propagation may vary depending on the type of non-normal distribution.

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