awarmle: Waring Modeling of Discrete Data
In degreenet: Models for Skewed Count Distributions Relevant to Networks

Description Usage Arguments Value Note References See Also Examples

Functions to Estimate the Waring Discrete Probability Distribution via maximum likelihood.

1 2	awarmle(x, cutoff = 1, cutabove = 1000, guess = c(3.5,0.1), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)

`x`	A vector of counts (one per observation).
`cutoff`	Calculate estimates conditional on exceeding this value.
`cutabove`	Calculate estimates conditional on not exceeding this value.
`guess`	Initial estimate at the MLE.
`conc`	Calculate the concentration index of the distribution?
`method`	Method of optimization. See "optim" for details.
`hellinger`	Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood.
`hessian`	Calculate the hessian of the information matrix (for use with calculating the standard errors.

`theta`	vector of MLE of the parameters.
`asycov`	asymptotic covariance matrix.
`asycor`	asymptotic correlation matrix.
`se`	vector of standard errors for the MLE.

conc

The value of the concentration index (if calculated).

See the working papers on http://www.csss.washington.edu/Papers for details

Jones, J. H. and Handcock, M. S. "An assessment of preferential attachment as a mechanism for human sexual network formation," Proceedings of the Royal Society, B, 2003, 270, 1123-1128.

ayulemle, awarmle, simwar

# Simulate a Waring distribution over 100
# observations with a PDf exponent of 3.5 and a 
# probability of including a new actor of 0.1

set.seed(1)
s4 <- simwar(n=100, v=c(3.5,0.1))
table(s4)

#
# Calculate the MLE and an asymptotic confidence
# interval for the parameters
#

s4est <- awarmle(s4)
s4est

# Calculate the MLE and an asymptotic confidence
# interval for rho under the Yule model
#

s4yuleest <- ayulemle(s4)
s4yuleest

#
# Compare the AICC and BIC for the two models
#

llwarall(v=s4est$theta,x=s4)
llyuleall(v=s4yuleest$theta,x=s4)