generatePoisson(lambda)
Overview
The generatePoisson(lambda) function generates a random number that follows a Poisson distribution.
Parameters
| Parameter | Type | Description |
|---|---|---|
lambda |
Number | The average rate of events per interval for the Poisson distribution. Must be greater than 0. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a Poisson distribution. |
Example
local result = StatBook.generatePoisson(5)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a Poisson distribution with parameter \lambda .
The probability mass function (pmf) of the Poisson distribution is defined as:
P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}
In this implementation, the algorithm uses a method based on direct simulation. It initializes a loop with p = 1 and multiplies p by a random number between 0 and 1 until p is less than or equal to e^{-\lambda} . The number of iterations minus 1 gives the random variable from the Poisson distribution.
\text{result} = k - 1