adqemle: Discrete version of q-Exponential Modeling of Discrete Data

Description

Functions to Estimate the Discrete version of q-Exponential Probability Distribution via maximum likelihood.

Usage

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

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).

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.

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 Discrete version of q-Exponential distribution over 100
# observations with a PDF exponent of 3.5 and a 
# sigma scale of 1

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

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

s4est <- adqemle(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
#

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