Is 2 times normal distribution still a normal distribution please?

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Discussion Overview

The discussion revolves around whether a modified probability density function (PDF) retains the properties of a normal distribution. Participants explore the implications of scaling a normal distribution and its relation to normalization and kurtosis.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions if the function 3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) qualifies as a normal distribution, given its mean and variance.
  • Another participant asserts that the function is not a normalized PDF since the total probability exceeds 1.
  • A participant inquires if using the form A exp(-x^2/B) with parameters A and B could lead to a normalized normal distribution after fitting.
  • It is stated that for any A, B > 0, the function A exp(-x^2/B), when normalized, will yield a normal distribution.

Areas of Agreement / Disagreement

Participants express differing views on the normalization of the initial function, with some agreeing on the conditions under which a modified function can represent a normal distribution.

Contextual Notes

The discussion does not resolve the normalization issue of the initial function, and the implications of kurtosis in relation to the modified distributions remain unclear.

wall_e
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Hi, it will be a very silly question, excuse me please.

I am wondering whether

3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) is still a normal distribution please?


where mean is 0, delta^2 is the variance.


Thank you very very much.

Also, how to understand this related to the kurtois please? Many many thanks again.
 
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It is not a normalized PDF, since the total probability sums up to more than 1.
 
thank you very much, pmsrw3.

So if I want to choose a form A exp(-x^2/B) to fit a pdf, where A and B are parameters, after normalization, I will get a normal distribution?
 
Yup, for any A,B > 0, A exp(-x^2/B), normalized, is a normal distribution.
 
Oh, thank you very much! pmsrw3
 

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