R: Moran's Log Spacings Test

moranTest {DistributionUtils} | R Documentation

## Moran's Log Spacings Test

### Description

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

### Usage

    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 θ is a vector of known parameters. This function implements the Cheng and Stephens(1989) extended Moran test for unknown parameters.

The test statistic is

T(thetahat)=(M(thetahat)+1/2k-C1)/C2

Where M(\hat θ), the Moran statistic, is

M(θ)=-(log(y_1-y_0)+log(y_2-y_1)+...+log(y_m-y_{m-1}))

M(theta)=-(log(y_1-y_0)+log(y_2-y_1)+...+log(y_m-y_m-1))

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).

### Value

`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.

### Author(s)

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

### 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.

### 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

[Package DistributionUtils version 0.6-0 Index]