degreenet (version 1.3-1)

ayulemle: 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

  • thetavector of MLE of the parameters.
  • asycovasymptotic covariance matrix.
  • asycorasymptotic correlation matrix.
  • sevector of standard errors for the MLE.
  • concThe value of the concentration index (if calculated).

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

Run this code
# 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)

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