moranTest function

Moran's Log Spacings Test

This function implements a goodness-of-fit test using Moran's log spacings statistic.

moranTest(x, densFn, param = NULL, ...)

Arguments

• densFn: Character. The root name of the distribution to be tested.
• x: Numeric. Vector of data to be tested.
• param: Numeric. A vector giving the parameter values for the distribution specified by densFn. If no param values are specified, then the default parameter values of the distribution are used instead.
• ...: Additional arguments to allow specification of the parameters of the distribution other than specified by param.

Details

Moran(1951) gave a statistic for testing the goodness-of-fit of a random sample of $x$-values to a continuous univariate distribution with cumulative distribution function $F(x, theta)$, where $\theta$ is a vector of known parameters. This function implements the Cheng and Stephens(1989) extended Moran test for unknown parameters.

The test statistic is

Where $M(\hat \theta)$, the Moran statistic, is

This test has null hypothesis: $H_0$ : a random sample of $n$ values of $x$ comes from distribution $F(x, theta)$, where $theta$ is the vector of parameters. Here $theta$ is expected to be the maximum likelihood estimate $thetahat$, an efficient estimate. The test rejects $H_0$ at significance level $alpha$ if $T(thetahat)$ > $chisq(alpha, df = n)$.

Returns

• statistic: Numeric. The value of the Moran test statistic.

• estimate: Numeric. A vector of parameter estimates for the tested distribution.

• parameter: Numeric. The degrees of freedom for the Moran statistic.

• p.value: Numeric. The p-value for the test. - data.name: Character. A character string giving the name(s) of the data.

• method: Character. Type of test performed.

References

Cheng, R. C. & Stephens, M. A. (1989). A goodness-of-fit test using Moran's statistic with estimated parameters. Biometrika, 76 , 385--92.

Moran, P. (1951). The random division of an interval---PartII. J. Roy. Statist. Soc. B, 13 , 147--50.

Author(s)

David Scott d.scott@auckland.ac.nz , Xinxing Li xli053@aucklanduni.ac.nz

Examples

### Normal Distribution
x <- rnorm(100, mean = 0, sd = 1)
muhat <- mean(x)
sigmahat <- sqrt(var(x)*(100 - 1)/100)
result <- moranTest(x, "norm", mean = muhat, sd = sigmahat)
result

### Exponential Distribution
y <- rexp(200, rate = 3)
lambdahat <- 1/mean(y)
result <- moranTest(y, "exp", rate = lambdahat)
result