WL: Statistical inference in weighted Lindley distribution

In WLinfer: Statistical Inference in Weighted Lindley Distribution

Statistical inference in weighted Lindley distribution

Description

Weighted Lindley distribution is suggested by Ghitany et al. (2011). WL provides four types of estimator, which are MME, modified MME, MLE, and MLEc from weighted Lindley distribution. And there are four sub-options, which are bias-correction, goodness of fit test, confidence interval, and Wilks' theorem test.

Usage

WL(
  x,
  est_method = "MLEc",
  bias_cor = "None",
  dist_test = "ks",
  gof_alpha = 0.05,
  ks_side = "two",
  CI_method = NULL,
  CI_scale = "normal",
  CI_side = "two",
  CI_alpha = 0.05,
  boot_iter = 10^3,
  wilks_test = TRUE,
  wilks_alpha = 0.05,
  wilks_side = "two"
)

Arguments

x	a numeric vector or data frame.
est_method	a character string which selects the estimation method ("MME", "MMEm", "MLE", "MLEc"), default is "MLEc".
bias_cor	an optional character character string which selects the bias correction method ("coxsnell", "boot" or "firth").
dist_test	a character string or character vector which choose the test of goodness of fit ("all","ks","ad","cvm").
gof_alpha	a numeric value between 0 and 1 for controlling the significance level of goodness of fit test; default value is 0.05.
ks_side	a character string which selects the alternative hypothesis ("two", "less" or "greater") for Kolmogorov-Smirnov Test, default is "two".
CI_method	a character string which selects the method for calculating confidence intervals ("asymp" or "boot"), confidence interval will not be printed with default. Since the "asymp" option is not available with bias correction, only the "boot" is available with bias correction.
CI_scale	a character string which selects the scale of confidence intervals ("exp" or "normal")
CI_side	a character string which selects the direction of confidence intervals ("two", "less" or "greater").
CI_alpha	a numeric value between 0 and 1 for controlling the significance level of confidence intervals; default value is 0.05.
boot_iter	a numeric value for iteration number of bootstrap method.
wilks_test	logical. If TRUE, wilks' theorem test is performed.
wilks_alpha	a numeric value between 0 and 1 for controlling the significance level of wilks' theorem test; default value is 0.05.
wilks_side	a character string which selects the direction of wilks' theorem test ("two", "less" or "greater").

Details

First, the user can determine the type of estimator from MME, modified MME, MLE, and MLEc. The closed form formulas for MME, modified MME, and MLEc are given in Hyoung-Moon Kim. et al. (2020). And MLE is obtained numerically. Additionally MLE and MLEc have bias correction options. MLE has Cox&Snell method and Firth's method, however MLEc has Cox&Snell method and bootstrap method.

Second, it provides a goodness of fit test. There are three kinds of tests, Kolmogorov-Smirnov test, Anderson Darling test, and Cramer-von Mises test. They provide statistics and also p-values. If the input value gof_alpha is selected, it determines whether or not to reject the null hypothesis.

Third, it provides information on the confidence interval. There are two kinds of confidence intervals, one is based on bootstrap method, and the other is asymptotic variance based method. Asymptotic variance based method is only available without bias correction, however bootstrap method is always available. Sometimes the confidence interval is outside the parameter space. If it occers, confidence interval will be calculated with log scale and show the exponential confidence interval of log scaled estimators. This option can also be used separately with selecting "exp" in CI_scale.

Lastly, through wilks.test, WL test the parameter space of estimators lambda and phi. There is an option for Wilks' theorem test, and that option provides options for the side of Wilks' theorem test.

Value

WL returns a list with these components:

data	a numeric vector the input values.
dataname	a character string the name of input values.
stat_summary	a numeric vector with min, 1st quantile, median, 3rd quantile, and max.
mean	a numeric value mean of input values.
var	a numeric value variance of input values.
est	a numeric vector with estimated lambda and phi.
lambda_var	a numeric value variance of estimated lambda.
phi_var	a numeric value variance of estimationed lambda.
bias_cor	a character string from bias correction method ("coxsnell","firth" or "boot").
est_method	a character string from estimation method ("MME", "MMEm", "MLE" or "MLEc").
boot_iter	a numeric value of bootstrap iteration.
test_list	a list with results of goodness of fit test.
CI_list	a list with confidence interval related outputs.
wilks_list	a list with results of wilks' test.

References

Ghitany, M., Alqallaf, F., Al-Mutairi, D., Husain, H. (2011). A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in Simulation 81: 1190-1201.

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

Wang, M., Wang, W. (2017). Bias-Corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution. Communications in Statistics Simulation and Computation 46: 530-545.

Examples

example <- lifetime_alum
result <- WL(example)
print(result)

result_boot <- WL(example, CI_method = "boot")
print(result_boot)

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