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)

Arguments

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.

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.

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)