Computes the quantile or inverse Poisson cumulative distribution function.


x = cdfPoissonInv(p, lambda)
  • p (NxK matrix) – Probabilities at which to compute the Poisson inverse cumulative distribution function. \(0 < p < 1\).
  • lambda (ExE conformable with p) – The mean parameter.

x (NxK matrix, Nx1 vector or scalar) – each value of x is the smallest integer such that the Poisson cumulative distribution function is equal to or exceeds the corresponding value of p.


Suppose that a hospital emergency department sees an average of 200 patients during the Friday evening shift. If the hospital wants to have enough staff on hand to handle the patient load on 95% of Friday evenings, how many patients do they need staff on hand for?

// Probability
p = 0.95;

// The average observations
lambda = 200;

// Call cdfPoissonInv
x = cdfPoissonInv(p, lambda);

After running above code, the hospital should expect to see 224 or few patients on 95% of Friday evenings.

x = 224


For invalid inputs, cdfPoissoninv() 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.