Poisson Distribution

FSPoissoninv(Lamada, Optional Random Number)

Excel does not supply an inverse Poisson function. The Poisson, like the binomial is not continuous and is defined only for discrete values. The function requires only one input, lambda, which is the mean of the distribution. The random probability is optional, if none is supplied the function will generate a random probability.The Poisson is not a continuous distribution. It is defined only for discrete values, similar to the Binomial distribution.

Table 1 shows the result of simulation of a Poisson distribution with a mean of 5. (Remember the formula in the cell is shown in green below the cell.) The optional random number was not supplied so the function supplied one. Table 2 shows the same function being used, but with a supplied random number, while the source here is Excel's rand() function it can be any random number generator.

Figure 1 shows the cumulative density function for the Poisson, with a Lambda of 5. Notice that the function is discrete and the vertical distances is the probability of a particular value. For a value of 3 the probability is 0.14037 for a value of 9 the probability is 0.03627.

Figure 2 shows the distribution function, displayed as column frequency distribution for the Poisson with a mean of 5. Notice that the distribution is skewed to the right.