Calculates expected values of the lower parts of Poisson distributions (R.W. Payne).
||Boundary of lower part of distribution|
||Means of the distributions|
||Saves the expected values|
||Saves the cumulative lower probabilities|
ELPOISSON calculates expected values of the lower parts of Poisson distributions. The calculation is for all values less than or equal to the value specified by the
BOUND option. The
MEANS parameter specifies a variate containing means of the distributions, or it can be set to a scalar if there is a single distribution. The expected values can be saved in either a variate or a scalar (to match the type of
MEANS) by the
EXPECTEDVALUES parameter. The corresponding cumulative lower probabilities can similarly be saved by the
The expected value for each mean is given by the sum, for
n running from one to
n * PRPOISSON(n; mean) / CLPOISSON(BOUND-1; mean)
Problems arise when the cumulative upper probability becomes very low. The calculation becomes unreliable, due to numerical round-off, for values less than 1.0 E-10. A missing value is then returned for the expected value, and a zero value for the cumulative lower probability.
CAPTION 'ELPOISSON example',\ 'Expected values for means 5-25 with a lower bound of 10.';\ STYLE=meta,plain VARIATE [VALUES=5...25] Means ELPOISSON [BOUND=10] Means; EXPECTEDVALUES=Expected; CLPROBABILITIES=Clpr PRINT Means,Expected,Clpr; DECIMALS=0,3,4