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In probability theory and statistics, the chi-square distribution is one of the most widely used theoretical probability distributions. It is used in statistical significance tests. It is useful, because it is relatively easy to show that certain probability distributions come close to it, under certain conditions. One of these conditions is that the null hypothesis must be true. Another one is that the different random variables (or observations) must be independent of each other.
Chernoff bound for the CDF and tail (1-CDF) of a chi-squared random variable with ten degrees of freedom (k = 10)
Approximate formula for median compared with numerical quantile (top). Difference between numerical quantile and approximate formula (bottom).
