lengthtest: Test for uniform distribution width.
In LeArEst: Border and Area Estimation of Data Measured with Additive Error

Description Usage Arguments Value Examples

Function lengthtest() tests the hypothesized uniform domain width against two-sided or one-sided alternatives from data contaminated with additive error. The additive error can be chosen as Laplace, Gauss or scaled Student distribution with 1 - 5 degrees of freedom.

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lengthtest(x, error = c("laplace", "gauss", "t1", "t2", "t3", "t4",
  "t5"), alternative = c("two.sided", "greater", "less"), sd = NULL,
  null.a = NULL, sd.est = c("MM", "ML"), conf.level = 0.95)

`x`	Vector of input data
`error`	A character string specifying the error distribution. Must be one of "laplace", "gauss", "t1", "t2", "t3", "t4", "t5". Can be abbreviated.
`alternative`	A character string specifying the alternative hypothesis, must be one of "two.sided", "greater" or "less". Can be abbreviated.
`sd`	Explicit error standard deviation. Needs to be given if `var.sd` is not given.
`null.a`	Specified null value being tested.
`sd.est`	A character string specifying the method of error standard deviation estimation. Must be given if `sd` is not given. Can be "MM" (Method of Moments) or "ML" (Maximum Likelihood).
`conf.level`	Confidence level of the confidence interval.

List containing:

error.type: A character string describing the type of the error distribution,
radius: Estimated half-width of uniform distribution,
sd.error: Error standard deviation, estimated or given,
conf.level: Confidence level of the confidence interval,
alternative: A character string describing the alternative hypothesis,
method: A character string indicating what method for testing was used (asymptotic distribution of MLE or likelihood ratio statistic),
conf.int: The confidence interval for half-width,
null.a: null value being tested,
p.value: p-value of the test,
tstat: the value of the test statistic.

# generate uniform data with additive error and run a hypothesis testing on it
sample_1 <- runif(1000, -1, 1)
sample_2 <- rnorm(1000, 0, 0.1)
sample <- sample_1 + sample_2
out <- lengthtest(x = sample, error = "gauss", alternative = "greater",
                  sd.est = "MM", null.a = 0.997, conf.level = 0.95)