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What is distribution value?
The distribution of a statistical data set (or a population) is a listing or function showing all the possible values (or intervals) of the data and how often they occur. The normal distribution is based on numerical data that is continuous; its possible values lie on the entire real number line.
Why we use distribution in statistics?
The distribution provides a parameterized mathematical function that can be used to calculate the probability for any individual observation from the sample space. This distribution describes the grouping or the density of the observations, called the probability density function.
How to compare two p-value distributions in practice?
For instance, if we want to test whether a p-value distribution is uniformly distributed (i.e. p-value uniformity test) or not, we can simulate uniform random variables and compute the KS test statistic. By repeating this process 1000 times, we will have 1000 KS test statistics, which gives us the KS test statistic distribution below.
How to compare a sample with a distribution?
When we compare a sample with a theoretical distribution, we can use a Monte Carlo simulation to create a test statistics distribution. For instance, if we want to test whether a p-value distribution is uniformly distributed (i.e. p-value uniformity test) or not, we can simulate uniform random variables and compute the KS test statistic.
How to compare two distributions in real life?
The red line is the actual test statistic and the green line is the test statistic for 1000 random normal variables. By inserting the KS test statistic for the actual sample (i.e. the red line), we can see that the actual KS test statistic is contained inside the distribution.
Are there any distributions that have the same parameters?
Not all distributions have the same parameters. For example, the normal distribution is described by the location and the scale while the Gamma distribution is described by the shape and scale. The parameters in Table 1 minimized the negative log-likelihood for each distribution.