# Estimating Gaussian parameters of a set of data points. I have a set of data points. When I draw a histogram of them, plotting their frequency of occurrence against them, I get a curve that looks like a normal curve. I am also able to perform test on the data set to know whether it follows a normal distribution or more precisely whether the population it comes from follows a normal probability distribution. I am using Shapiro Wilk test for it.

Estimating Gaussian parameters of a set of data points
I have a set of data points. When I draw a histogram of them, plotting their frequency of occurrence against them, I get a curve that looks like a normal curve. I am also able to perform test on the data set to know whether it follows a normal distribution or more precisely whether the population it comes from follows a normal probability distribution. I am using Shapiro Wilk test for it.
However, how can I know what the equation of that normal curve will be? Moreover, is there a way I can test whether other standard distributions fit the points more accurately, and estimate their parameters?
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Step 1
You can estimate the parameters $\mu$ and $\sigma$ by using the statistics:
$\stackrel{^}{\mu }=\overline{X}=\frac{1}{n}\sum {X}_{i}$
and
${\stackrel{^}{\sigma }}^{2}=\frac{1}{n-1}\sum \left({X}_{i}-\overline{X}{\right)}^{2}$
Step 2
Where ${X}_{i}$ would be the ith sample element. Thus $\overline{X}$ is the sample mean. So the equation of the fitted distribution would be:
$f\left(x\right)=\frac{1}{\sqrt{2\pi {\stackrel{^}{\sigma }}^{2}}}{e}^{-\frac{\left(x-\stackrel{^}{\mu }{\right)}^{2}}{2{\stackrel{^}{\sigma }}^{2}}}$
You can use the Pearson Chi Squared test to check the hypothesis that the data comes from the distribution being tested.