interval_var1 {OneTwoSamples}

Two sided interval estimation of sigma^2 of one normal sample

Description

Compute the two sided interval estimation of sigma^2 of one normal sample when the population mean is known or unknown.

Usage

interval_var1(x, mu = Inf, alpha = 0.05)

Arguments

x

A numeric vector.

mu

The population mean. When it is known, input it, and the function computes the interval endpoints using a chi-square distribution with degree of freedom n. When it is unknown, ignore it, and the function computes the interval endpoints using a chi-square distribution with degree of freedom n-1.

alpha

The significance level, a real number in [0, 1]. Default to 0.05. 1-alpha is the degree of confidence.

Value

A data.frame with variables:

var

The estimate of the population variance. When the population mean mu is known, var = mean((x-mu)^2). When mu is unknown, var = var(x).

df

The degree of freedom.

a

The confidence lower limit.

b

The confidence upper limit.

Author(s)

Ying-Ying Zhang (Robert) [e-mail]

References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, doi:10.2991/asshm-13.2013.29.

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
interval_var1(x, mu = 1)
interval_var1(x)