Calculates expected values of the lower parts of negative binomial distributions (R.W. Payne).
Options
BOUND = variate or scalar |
Boundary of upper part of distribution |
Parameters
MEANS = variates or scalar |
Means of the distributions |
AGGREGATION = scalars |
Aggregation parameter for the distributions |
EXPECTEDVALUES = variates or scalar |
Saves the expected values |
CLPROBABILITIES = variates or scalar |
Saves the cumulative lower probabilities |
Description
ELNEGBINOMIAL calculates expected values of the lower parts of negative binomial distributions. The calculation is for all values less than or equal to the value specified, in either a scalar or a variate, 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. If BOUND and MEANS are variates, they must both be the same length. The AGGREGATION parameter specifies a scalar containing their aggregation parameter. 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.
Options: BOUND.
Parameters: MEANS, AGGREGATION , EXPECTEDVALUES, PROBABILITIES
Method
The expected value for each mean is given by the sum, for n running from one to BOUND, of
n * PRNEGATIVEBINOMIAL(n;mean) / CLNEGATIVEBINOMIAL(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
Directives: DISTRIBUTION
Procedures: EUNEGBINOMIAL ELGAMMA EUGAMMA ELPOISSON EUPOISSON RNBTOBIT
GenStat Reference Manual 1 Summary section on: Basic and nonparametric statistics.
Example
CAPTION ' 'ELNEGBINOMAL example',!t('Expected values for means 5-25',\
'with a lower bound of 10, and aggregation parameter 2.');\
STYLE=meta,plain
VARIATE [VALUES=5...25] Means
ELNEGBINOMIAL [BOUND=10] Means; AGGREGATION=2; EXPECTEDVALUES=Expected;\
CLPROBABILITIES=Clpr
PRINT Means,Expected,Clpr; DECIMALS=0,3,4