Poisson cumulative distribution function
lambda can be scalars, vectors,
matrices, or multidimensional arrays that all have the same size. If only one argument is a
poisscdf expands it to a constant array with the same dimensions
as the other argument.
Compute and plot the Poisson cumulative distribution function for the specified range of integer values and average rate.
A computer hard disk manufacturing facility performs random tests of individual hard disks. The policy is to shut down the manufacturing process if an inspector finds more than four bad sectors on a disk. Assuming that on average a disk has two bad sectors, find the probability of a manufacturing process shutdown after the first inspection.
1 - poisscdf(4,2)
ans = 0.0527
Compute the probabilities a manufacturing process shutdown after the first inspection if on average a disk has 0, 1, 2, ..., 10 bad sectors.
lambda = 0:10; y = 1 - poisscdf(4,lambda);
Plot the results.
scatter(lambda,y,'Marker',"o") grid on
Compute the complement of the Poisson cumulative distribution function with more accurate upper tail probabilities.
A computer hard disk manufacturing facility performs random tests of individual hard disks. Assuming that on average a disk has 10 bad sectors, find the probability that a disk has more than 100 bad sectors.
format long 1 - poisscdf(100,10)
ans = 0
This result shows that
poisscdf(100,10) is so close to 1 (within
eps) that subtracting it from 1 gives 0. To approximate the extreme upper tail probabilities better, compute the complement of the Poisson cumulative distribution function directly instead of computing the difference.
ans = 5.339405460719755e-64
x— Values at which to evaluate Poisson cdf
Values at which to evaluate the Poisson cdf, specified as a scalar value or array of scalar values.
lambda— Rate parameters
Rate parameters, specified as a positive value or array of positive values. The rate parameter indicates the average number of events in a given time interval.
The Poisson cumulative distribution function lets you obtain the probability of an event occurring within a given time or space interval less than or equal to x times if on average the event occurs λ times within that interval.
The Poisson cumulative distribution function for the given values x and λ is
poisscdf is a function specific to Poisson distribution.
Statistics and Machine Learning Toolbox™ also offers the generic function
cdf, which supports various probability distributions. To use
cdf, specify the probability distribution name and its parameters.
Alternatively, create a
PoissonDistribution probability distribution
object and pass the object as an input argument. Note that the distribution-specific
poisscdf is faster than the generic function
Use the Probability Distribution Function app to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).