Computes the Poisson cumulative distribution function.


p = cdfPoisson(x, lambda)
  • x (NxK matrix, Nx1 vector or scalar) – Values at which to evaluate the cumulative distribution function for the Poisson distribution. \(x > 0\).
  • lambda (ExE conformable with x) – The mean parameter.

p (NxK matrix, Nx1 vector or scalar) – Each element in p is the cumulative distribution function of the Poisson distribution evaluated at the corresponding element in x.


Suppose that a hospital emergency department sees and average of 200 patients during the Friday evening shift. What is the probability that they will see fewer than 250 patients during any one Friday evening shift.

// The mean parameter
lambda = 200;

// Value to compute cdf
x = 250;

p = cdfPoisson(x, lambda);

After running above code,

p = 0.99971538 or 99.715%


For invalid inputs, cdfPoisson() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.