hytest (version 0.1.1)

norm_errorI: Empirical Error Type I Associated with a Normal Distribution

Description

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

Usage

norm_errorI(c = 1, n = 100, theta0 = 0, sd = 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 Normal distribution. Default value is 0.

sd

numeric, represents the scale parameter of a Normal 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 70 from an Normal distribution,
# a critical value c = 0.65 and R = 20000 to test H_0: theta = 0 vs H_1: theta != 0
norm_errorI(0.65,70,theta0=0,sd=1,R=20000)