Why errors are assumed to be normaly distributed?
Errors are assumed to be normally distributed for a few reasons:
1. Many real-world phenomena can be modeled using a normal distribution. This includes errors in measurements, observations, and forecasts.
2. The central limit theorem states that as the sample size increases, the distribution of the sample mean tends towards normality regardless of the underlying distribution of the data. This means that even if the errors are not normally distributed, their means (sample means) are likely to be normally distributed.
3. Assumption of normal distribution of errors can simplify and improve statistical analyses. For example, the use of normal distribution assumptions allows for the use of parametric tests, which are more powerful and efficient than non-parametric tests.
Overall, the assumption of normal distribution of errors simplifies modeling and enables the use of powerful statistical tests.