Continuous Uniform Sum Random Variable Generator

The continuous uniform sum distribution is the sum of k continuous uniform random variables that are bounded between a and b. When k = 1, the distribution is uniform; when k = 2, the distribution is triangular. As k grows, the uniform sum distribution approaches the normal distribution with a mean of k(a+b)/2 and a variance of k(b-a)²/12.

You can use the tool below to generate N random variables from a continuous uniform sum distribution.

a (min) =     b (max) =     k = N =
Decimal Precision integer tenths hundredths thousandths	Display comma separated vertical

The mean, median, mode, variance, and skewness of the continuous uniform sum distribution are:

mean = k(a+b)/2
median = k(a+b)/2
mode = k(a+b)/2     if k is at least 2
variance = k(b-a)²/12
skewness = 0

One way to approximate the standard normal distribution with the uniform sum distribution is to set a = b = 0.5 and k = 12. This gives a symmetric bell-shaped probability curve with a mean of 0 and variance of 1.

For dice simulation and other discretely valued sums, use the Discrete Uniform Sum Distribution Random Variable Generator instead of the calculator above.

If you try to use the tool above to simulate dice by setting min = 1, max = 6, and decimal precision = integer, you will generate a discrete sum distribution in which the tail-end values (k and 6k) are under-weighted. This will not give you an accurate simulation.

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