Gamma Distribution Random Generator
Generate random numbers from a gamma distribution with shape k and scale theta. Shows a sample list, histogram, sample mean and sample variance.
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Input
Enter the shape parameter k, the scale parameter theta and the number of samples, then press generate to draw random numbers from a gamma distribution.
k
theta
samples
You can choose from 1 to 10000 samples.
Result
Enter the parameters and press generate to see the random numbers and histogram here.
How it works
- Enter the shape parameter k (k greater than 0), the scale parameter theta (theta greater than 0) and the number of samples, then press the generate button to draw random numbers from a gamma distribution. New samples are produced each time you press the button.
- Samples are generated with the Marsaglia-Tsang method. It is valid when the shape k is at least 1, so for k below 1 the value is drawn with shape k plus 1 and corrected by multiplying with a uniform variate raised to the power one over k. Standard normal variates come from the Box-Muller method.
- The theoretical mean of a gamma distribution is k times theta, and the theoretical variance is k times theta times theta. The sample mean and sample variance of the generated numbers approach these theoretical values, and the agreement improves as the count grows.
- The histogram splits the range from the minimum to the maximum sample into equal-width intervals and shows the frequency of each interval as a bar. The number of intervals is chosen automatically based on the count, up to 20 intervals.
- You can generate up to 10000 samples. Only the first part of the sample list is shown, and the remaining values are reported as a count. Use this tool for statistics study and for checking simulation behavior.
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