Estimating Gaussian parameters of a set of data pointsI 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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metodikkf6z · Accepted Answer

Step 1You can estimate the parameters   μ and   σ by using the statistics:            μ      ^        =            X      ¯        =      1    n    ∑      X    i  and                    σ        ^              2    =      1          n      −      1        ∑  (      X    i    −            X      ¯            )    2  Step 2Where       X    i   would be the ith sample element. Thus             X      ¯       is the sample mean. So the equation of the fitted distribution would be:  f  (  x  )  =            1              2        π                                            σ              ^                                2                          e          −                                    (            x            −                                          μ                ^                                                    )              2                                            2                                                            σ                  ^                                            2                                          You can use the Pearson Chi Squared test to check the hypothesis that the data comes from the distribution being tested.

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