gyulemle: Models for Count Distributions

In degreenet: Models for Skewed Count Distributions Relevant to Networks

Models for Count Distributions

Description

Functions to Estimate Parametric Discrete Probability Distributions via maximum likelihood Based on categorical response

Usage

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

Arguments

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.
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

result	vector of parameter estimates - lower 95% confidence value, upper 95% confidence value, the PDF MLE, the asymptotic standard error, and the number of data values >=cutoff and <=cutabove.
theta	The Yule MLE of the PDF exponent.
value	The maximized value of the function.
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.

Examples

#
# 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)

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