ayulemle: Yule Distribution Modeling of Discrete Data

In degreenet: Models for Skewed Count Distributions Relevant to Networks

Yule Distribution Modeling of Discrete Data

Description

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

Usage

ayulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE,
     method = "BFGS", hellinger = FALSE, hessian = TRUE, weights = rep(1, length(x)))

Arguments

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.
weights	sample weights on the observed counts.

Value

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).

Note

See the papers on https://handcock.github.io/?q=Holland for details

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.

See Also

ayulemle, awarmle, simyule

Examples

# Simulate a Yule distribution over 100
# observations with PDf exponent of 3.5

set.seed(1)
s4 <- simyule(n=100, rho=3.5)
table(s4)

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

s4est <- ayulemle(s4)
s4est

#
# Compute the AICC and BIC for the model
#

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

degreenet documentation built on Sept. 26, 2024, 1:08 a.m.