ELPOISSON Procedure

Calculates expected values of the lower parts of Poisson distributions (R.W. Payne).

Option

Parameters

 Description

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 CLPROBABILITIES parameter.

An important use of ELPOISSON is to provide estimates for censored Poisson observations for the RTOBITPOISSON, GLTOBITPOISSON and HGTOBITPOISSON procedures.

Option: BOUND.
Parameters: MEANS, EXPECTEDVALUES, CLPROBABILITIES.

Method

The expected value for each mean is given by the sum, for n running from one to BOUND, of

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.

See also

Directive: DISTRIBUTION.
Procedures: EUPOISSON, RTOBITPOISSON, GLTOBITPOISSON, HGTOBITPOISSON.
Commands for: Basic and nonparametric statistics.

Example

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