CoxSnell_bias: Cox & Snell bias correction methods for estimators

In WLinfer: Statistical Inference in Weighted Lindley Distribution

Cox & Snell bias correction methods for estimators

Description

CoxSnell_bias and CoxSnell_bias_log provide a vector of MLE bias, and it can be used for bias correction of both MLE and MLEc. The estimation method was suggested by by Cox and Snell(1968).

Usage

CoxSnell_bias(n, lambda, phi)

CoxSnell_bias_log(n, lambda, phi)

Arguments

n	a numeric value of data length.
lambda	a numeric value of estimated lambda.
phi	a numeric value of estimated phi.

Details

CoxSnell_bias provides the bias of original lambda and phi. However, CoxSnell_bias_log provides the bias of log lambda and log phi. In some cases, estimators are smaller than bias, and it means that the bias corrected estimators are out of parameter space. To solve this problem, CoxSnell_bias_log is useful. Correction formula is based on Fisher information and some cumulants, which are given in Kim and Jang (2020).

Value

A numeric vector of Cox & Snell biases of lambda and phi.

Background

These functions implement formulas given in Hyoung-Moon Kim. et al. (2020).

References

Hyoung-Moon Kim. and Yu-Hyeong Jang. (2020). New Closed-Form Estimators for Weighted Lindley Distribution. , submitted.

Examples

data <- fail_fiber
mlec <- MLEc_WL(data)
n <- length(data)
CoxSnell_bias(n, mlec[1], mlec[2])
CoxSnell_bias_log(n, mlec[1], mlec[2])

WLinfer documentation built on Sept. 2, 2022, 9:06 a.m.