In a Java program, how can I determine if a dataset has the following or not a normal distribution?
Is it possible?
Is there an API or algorithm that I can use that defines this?
There are two questions here: how to determine if the distribution is normal and how to do it in Java . As the first link will show you, there are varying degrees of how confident you are that you are looking at ordinary data from formal to informal. The second link shows that there are no standard Java packages for statistical analysis, but many other ways to implement them.
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As others have noted, determining that data points come from a normal distribution is much more complicated.
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