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?
You can estimate the parameters $\mu$ and $\sigma$ by using the statistics: $$\hat{\mu}=\bar{X}=\frac{1}{n}\sum X_i$$ and $$\hat{\sigma}^2=\frac{1}{n-1}\sum(X_i-\bar{X})^2$$
Where $X_i$ would be the $i$th sample element. Thus $\bar{X}$ is the sample mean. So the equation of the fitted distribution would be: $$f(x)=\dfrac{1}{\sqrt{2\pi\hat{\sigma}^2}}e^{-\dfrac{(x-\hat{\mu})^2}{2\hat{\sigma}^2}}$$ You can use the Pearson Chi Squared test to check the hypothesis that the data comes from the distribution being tested.