lengthtest function

Test for uniform distribution width.

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.

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)

Arguments

• 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.

Returns

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.

Examples

# 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)