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 sticky 2022-09-19 23:50

Gaussian Distribution

Hello Folks,

I was going through some articles and found a statement that is not very clear to me.

The statement goes as below:

"The CDF of a Gaussian distribution can be expressed as a linear if the graph is drawn in a sigma-scale for the y-axis"

I having a hard-time understanding the statement and process of have to convert the CDF to linear scale.

Regards

 MattcAnderson 2022-09-22 18:23

Hi Sticky and others,

A Gaussian distribution, or bell curve can be characterized by two variables.
First is its mean, or center value.
Second is its standard distribution, or wideness.

See wikipedia
[URL="https://en.wikipedia.org/wiki/Normal_distribution"]https://en.wikipedia.org/wiki/Normal_distribution[/URL]

Have a nice day.
Matt

 MattcAnderson 2022-09-22 21:28

Also,
I did a Google search for "CDF normal distribution"
[URL="https://www.probabilitycourse.com/chapter4/4_2_3_normal.php"]https://www.probabilitycourse.com/chapter4/4_2_3_normal.php[/URL]

Have a nice day.
Matt

 sticky 2022-09-25 15:32

Hello MattcAnderson,

Thanks for the reply,I understand what CDF and Gaussian distribution are.
What I dont understand is " graph is drawn in a sigma-scale for the y-axis"".

CDF drawn with sigma-scale for y -axis?

Regards
Sundeep

 Batalov 2022-09-25 17:54

[QUOTE=sticky;614119]What I dont understand is " graph is drawn in a sigma-scale for the y-axis"".
[/QUOTE]
It is easy to understand by analogy. Suppose you have some variable that has an exponential behavior (for example any biological effect that is measured by luminescence, e.g. gene expression). To make it look linear, you change the plot to have y-axis transformed by the function [U]inverse[/U] to exponent. What function is this? It is log().

Same here. CDF is known to have a wave-like, monotone function, usually denoted 𝛷() that describes it (when underlying distribution is normal). How do you transform y-axis? You apply the inverse function 𝛷[SUP]-1[/SUP](). It doesn't have an analytic expression but that doesn't matter - you can use a function that is indistinguishable from precise function, within pixels on your screen - you will not know the difference. So that's what programs like SigmaPlot do. It is rather simple.

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