ELBIG: The Parameter Estimation for Re-parameterized Length-Biased...

In wikanda-phaphan/ELBIG: The Parameter Estimation for Re-parameterized Length-Biased Inverse Gaussian Distribution

Description

The package ELBIG provides functions for parameter estimation for re-parameterized length-biased inverse Gaussian distribution with two estimation methods: the maximum likelihood method, the method of moments.

Usage

MME(X)
MLE(X)
Mill_Vibration

Arguments

X	vector of data.
n	a number of observations.
lambda	a value of the parameter lambda.
theta	a value of the parameter theta.

Details

Re-parameterized Length-Biased Inverse Gaussian (LBIG) Distribution

Define X as a positive random variable with the length-biased inverse Gaussian distribution based on Ahmed et al. (2008). A density function can be written in this form:

fLBIG=(1/(theta*sqrt(2*pi)))*((theta/X)^(1/2))*exp(-0.5*(sqrt(X/theta)-(lambda*sqrt(theta/X)))), where lambda, theta>0.

Value

The Parameter Estimation for Re-parameterized Length-Biased Inverse Gaussian Distribution

MME	gives the value of parameter estimates by the method of moments.
MLE	gives the value of parameter estimates by the maximum likelihood method.
Mill_Vibration	gives the vibration of the vertical roller mill in 60 minutes, contains the time (a.m.) and values of mill vibration (um), collected on 10 February 2019 from Phaphan (2021).

References

Folks, J. L. & Chhikara, R. S. (1978). The inverse Gaussian distribution and its statistical application - a review. Journal of the Royal Statistical Society.Serie B, 40, 263–289.

Ahmed, S.E., Budsaba, K., Lisawadi, S., & Volodin, A. (2008). Parametric estimation for the Birnbaum-Saunders lifetime distribution based on new parametrization. Thailand Statistician, 6(2), 213-240.

Phaphan, W. (2021). R package for the two-parameters crack distribution. International Journal of Mathematics and Computer Science, 16(4), in press.

Examples

#install.packages("devtools")
library(devtools)
#install_github("wikanda-phaphan/ELBIG")
library(ELBIG)

? ELBIG
########
X <- c(7.7,1.2,4,2,0.5)
MLE(X)
$Lamdahat
[1] 0.7767996
$Thetahat
[1] 1.733454

MME(X)
$Lamdahat
[1] 1.090257
$Thetahat
[1] 1.473503

wikanda-phaphan/ELBIG documentation built on Dec. 23, 2021, 5:14 p.m.