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

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.

References

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

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
#>  [1] 1.1584902 1.3630062 0.8126055 1.1722601 1.1243280 0.5711336 1.0969443
#>  [8] 0.9105451 1.1092194 1.2888373
interval_var1(x, mu = 1)
#>         var df          a         b
#> 1 0.0533823 10 0.02606153 0.1644064
interval_var1(x)
#>         var df          a         b
#> 1 0.0552148  9 0.02612308 0.1840228