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

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

Usage

interval_var3(x, mu = Inf, side = 0, 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.
side: A parameter used to control whether to compute two sided or one sided interval estimation. When computing the one sided upper limit, input side = -1; when computing the one sided lower limit, input side = 1; when computing the two sided limits, input side = 0 (default).
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] 0.9416208 0.8444366 0.9302892 1.2023435 0.9370456 0.9989236 0.7283394
#>  [8] 1.3145855 0.7601232 0.9854689
interval_var3(x, mu = 1, side = -1)
#>          var df a          b
#> 1 0.03078906 10 0 0.07813888
interval_var3(x)
#>          var df          a         b
#> 1 0.03279536  9 0.01551605 0.1093021