hytest (version 0.1.1)

gumbel_errorI: Empirical Error Type I Associated with a Gumbel Distribution

Description

gumbel_errorI is used to obtain an empirical error type I when we use a random sample from a Gumbel distribution.

Usage

gumbel_errorI(c = 1, n = 150, theta0 = 0, sigma = 1, R = 15000)

Value

A list with number of replicates, sample size, and critical value that were used in the calculation of error type I associated with a likelihood ratio statistic.

Arguments

c

numeric, represents a positive value that defines a critical region. Default value is 1.

n

numeric, represents the size of the sample. Default value is 100.

theta0

numeric, represents the location parameter under the null hypothesis of a sample from a Gumbel distribution. Default value is 0.

sigma

numeric, represents the scale parameter of a Gumbel distribution. It is assumed known and its default value is 1.

R

numeric, represents the number of replicates. Default value is 15000.

Author

Carlos Alberto Cardozo Delgado <[e-mail]>.

References

Casella, G. and Berger, R. (2003). Statistical Inference, Second Edition. Duxbury Press.

Hogg, R., McKean, J., and Craig, A. (2019) Introduction to Mathematical Statistic. Eighth edition. Pearson.

Examples

# Error type I when we use a random sample of size 150 from a Gumbel distribution,
# a critical value c = 0.5 and R = 500 to test H_0: theta = 3 vs H_1: theta != 3
library(gamlss.dist)
gumbel_errorI(0.5,n=150,theta0=3,R=500)