bsyule: Calculate Bootstrap Estimates and Confidence Intervals for the Yule Distribution

Description

Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Yule Distribution.

Usage

bsyule(x, cutoff=1, m=200, np=1, alpha=0.95, v=NULL,
                   hellinger=FALSE, cutabove=1000)
bootstrapyule(x,cutoff=1,cutabove=1000,
                          m=200,alpha=0.95,guess=3.31,hellinger=FALSE,
                          mle.meth="ayulemle")

Value

dist: matrix of sample CDFs, one per row.
obsmle: The Yule MLE of the PDF exponent.
bsmles: Vector of bootstrap MLE.
quantiles: Quantiles of the bootstrap MLEs.
pvalue: p-value of the Anderson-Darling statistics relative to the bootstrap MLEs.
obsmands: Observed Anderson-Darling Statistic.
meanmles: Mean of the bootstrap MLEs.

Arguments

x: A vector of counts (one per observation).
cutoff: Calculate estimates conditional on exceeding this value.
m: Number of bootstrap samples to draw.
np: Number of parameters in the model (1 by default).
alpha: Type I error for the confidence interval.
v: Parameter value to use for the bootstrap distribution. By default it is the MLE of the data.
hellinger: Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood.
cutabove: Calculate estimates conditional on not exceeding this value.
guess: Initial estimate at the MLE.
mle.meth: Method to use to compute the MLE.

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

# Now, 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

#
# Use the bootstrap to compute a confidence interval rather than using the 
# asymptotic confidence interval for rho.
#

bsyule(s4, m=20)