ptsuite (version 1.0.0)

alpha_mle: Estimating the Shape Parameter by Method of Maximum Likelihood (MLE)

Description

This function can be used to estimate the shape parameter using the Maximum Likelihood Estimator method (Newman 2005). It can be used to obtain biased and unbiased estimates of the shape and scale parameters as well as the confidence interval for the shape parameter for the biased estimates.

Usage

alpha_mle(dat, biased = TRUE, significance = NULL)

Arguments

dat

vector of observations

biased

TRUE/FALSE to indicate biased or unbiased estimates

significance

level of significance

Value

A list of the following form:

shape

Estimate of the shape parameter of the data

lower_bound

Upper error bound of the estimate of shape

upper_bound

Lower error bound of the estimate of shape

scale

Estimate of the scale parameter of the data (which is taken to be the minimum of the data)

References

Newman MEJ (2005). "Power Laws, Pareto Distributions And Zipf's Law." Contemporary Physics, 46, 323-351.

Examples

# NOT RUN {
x <- generate_pareto(10000, 5, 2)
alpha_mle(x, TRUE, 0.05)

x <- generate_pareto(10000, 5, 2)
alpha_mle(x, FALSE)

# }