llyule: Calculate the Conditional log-likelihood for Count Distributions

Description

Functions to Estimate the Conditional Log-likelihood for Discrete Probability Distributions. The likelihood is calcualted condition on the count being at least the cutoff value and less than or equal to the cutabove value.

Usage

llyule(v, x, cutoff=1,cutabove=1000, xr=1:10000 ,hellinger=FALSE,
       weights = rep(1, length(x)))

Value

the log-likelihood for the data x at parameter value v

(or the Hellinder distance if hellinger=TRUE).

Arguments

v: A vector of parameters for the Yule (a 1-vector - the scaling exponent).
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.
xr: range of count values to use to approximate the set of all realistic counts.
hellinger: Calculate the Hellinger distance of the parametric model from the data instead of the log-likelihood?
weights: sample weights on the observed counts.

References

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.

Examples

Run this code


# Simulate a Yule distribution over 100
# observations with rho=4.0

set.seed(1)
s4 <- simyule(n=100, rho=4)
table(s4)

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

s4est <- ayulemle(s4)
s4est

#
# Calculate the MLE and an asymptotic confidence
# interval for rho under the Waring model (i.e., rho=4, p=2/3)
#

s4warest <- awarmle(s4)
s4warest

#
# Compare the log-likelihoods for the two models
#

llyule(v=s4est$theta,x=s4)
llwar(v=s4warest$theta,x=s4)