Two sided interval estimation of sigma1^2 / sigma2^2 of two normal samples

Compute the two sided interval estimation of sigma1^2 / sigma2^2 of two normal samples when the population means are known or unknown.

Usage

interval_var2(x, y, mu = c(Inf, Inf), alpha = 0.05)

Arguments

x: A numeric vector.
y: A numeric vector.
mu: The population means. When it is known, input it, and the function computes the interval endpoints using an F distribution with degree of freedom (n1, n2). When it is unknown, ignore it, and the function computes the interval endpoints using an F distribution with degree of freedom (n1-1, n2-1).
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:

rate: The estimate of the ratio of population variances, rate = Sx2/Sy2. When the population means mu is known, Sx2 = 1/n1*sum((x-mu[1])^2) and Sy2 = 1/n2*sum((y-mu[2])^2. When mu is unknown, Sx2 = var(x) and Sy2 = var(y).
df1: The first degree of freedom.
df2: The second 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] 1.0337024 1.0478129 1.0472643 0.9481762 1.1298091 0.7564718 1.1683941
#>  [8] 0.6761579 1.0528332 1.0194621
y=rnorm(20, mean = 2, sd = 0.3); y
#>  [1] 2.5366596 1.7033952 2.5672710 2.3602482 1.4560367 2.1111297 1.8551970
#>  [8] 2.0303853 2.0117232 2.3194477 0.8870452 2.4800535 2.3539010 1.2048454
#> [15] 1.7675672 2.1817633 1.9099158 2.3031477 1.4691850 2.2016608
interval_var2(x, y, mu = c(1,2))
#>        rate df1 df2          a         b
#> 1 0.1105592  10  20 0.03986024 0.3779515
interval_var2(x, y)
#>        rate df1 df2          a         b
#> 1 0.1160633   9  19 0.04029904 0.4275005