llgyuleall: Calculate the log-likelihood for Count Distributions

Description

Functions to Estimate the Log-likelihood for Discrete Probability Distributions Based on Categorical Response.

Usage

llgyuleall(v, x, cutoff = 2, cutabove = 1000,  np=1)

Value

the log-likelihood for the data x at parameter value v.

Arguments

v: A vector of parameters for the Yule (a 1-vector - the scaling exponent).
x: A vector of categories for counts (one per observation). The values of x and the categories are: 0=0, 1=1, 2=2, 3=3, 4=4, 5=5-10, 6=11-20, 7=21-100, 8=>100
cutoff: Calculate estimates conditional on exceeding this value.
cutabove: Calculate estimates conditional on not exceeding this value.
np: wnumber of parameters in the model. For the Yule this is 1.

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 Yule distribution over 100
# observations with rho=4.0
#

set.seed(1)
s4 <- simyule(n=100, rho=4)
table(s4)

#
# Recode it as categorical
#

s4[s4 >  4 & s4 < 11] <- 5
s4[s4 > 100] <- 8
s4[s4 >  20] <- 7
s4[s4 >  10] <- 6


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

s4est <- gyulemle(s4)
s4est

# Calculate the MLE and an asymptotic confidence
# interval for rho under the Waring model (i.e., rho=4, p=2/3)
#

s4warest <- gwarmle(s4)
s4warest

#
# Compare the AICC and BIC for the two models
#

llgyuleall(v=s4est$theta,x=s4)
llgwarall(v=s4warest$theta,x=s4)