Package 'DistributionTest' reference manual

Title:	Powerful Goodness-of-Fit Tests Based on the Likelihood Ratio
Description:	Provides new types of omnibus tests which are generally much more powerful than traditional tests (including the Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests),see Zhang (2002) <doi:10.1111/1467-9868.00337>.
Authors:	Ning Cui [aut, cre], Maoyuan Zhou [ctb]
Maintainer:	Ning Cui <[email protected]>
License:	GPL (>= 3)
Version:	1.1
Built:	2024-10-24 03:12:33 UTC
Source:	https://github.com/cran/DistributionTest

perform a one- or two-sample analogue ZA of Anderson-Darling statistic

Description

The new statistics ZA appear similar to the Anderson-Darling, but it's generally much more powerful,see Jin Zhang(2002).

Usage

za.test(x, y, para = NULL, N = 1000)
za.test(x, y, para = NULL, N = 1000)

Arguments

`x`	a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed.
`y`	When tested as a single sample, a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. When tested as two-sample, a character string indicating what type of test was performed. Distributions "unif", "exponential", "normal", "lognormal", "gamma","t" and "weibull" are recognised.Here,the names of "exponential", "normal" and "lognormal" are simplified as "exp" ,"norm" and "lognorm" respectively.
`para`	A named list giving the parameters of the distribution specified and this can be omitted.
`N`	The number of replications in Monte Carlo simulation.The default value is 1000

Details

The ZA test is an EDF omnibus test for the composite hypothesis of distribution. The test statistic is

$Za = -\sum_{i=1}^{n}[\frac{\ln[F_{0}(X_{(i)})]}{n-i+0.5}+\frac{\ln[1-F_{0}(X_{(i)})]}{i-0.5}],$

where $F_{0}(x)$ is a hypothesized distribution function to be tested.Here, $F_{0}(X_{(i)}) = \Phi(x)$ , $\Phi$ is the cumulative distribution function of the specificed distribution.The p-value is computed by Monte Carlo simulation.

Value

A list with class “htest” containing the following components:

`statistic`	the value of the ZA statistic.
`p.value`	the p-value for the test.
`method`	the character string “ZA test for given distribution”.
`data.name`	a character string giving the name(s) of the data.

Note

The Za test is the recommended EDF test by Jin Zhang.

Author(s)

Ning Cui

References

Jin Zhang: Goodness-of-Fit Tests Based on the Likelihood Ratio.Journal of the Royal Statistical Society,64,281-294.

Jin Zhang,Yuehua Wu: Likelihood-ratio tests for normality.Computational Statistics & Data Analysis,49,709-721.

Jin Zhang: Powerful Two-Sample Tests Based on the Likelihood Ratio. Technometrics, 48:1, 95-103.

Examples

x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
za.test(x,y)
za.test(x,"unif")
za.test(x,"norm")
za.test(x,"unif",para = list(min=1,max=2))
za.test(x,"exp",para = list(rate=1))
za.test(x,"norm",para = list(mean=1,sd=2))
za.test(x,"lognorm",para = list(mean=1,sd=2))
za.test(x,"weibull",para = list(shape=1,scale=2))
za.test(x,"gamma",para = list(shape=2,scale=1))
za.test(x,"t",para = list(df=3))
x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
za.test(x,y)
za.test(x,"unif")
za.test(x,"norm")
za.test(x,"unif",para = list(min=1,max=2))
za.test(x,"exp",para = list(rate=1))
za.test(x,"norm",para = list(mean=1,sd=2))
za.test(x,"lognorm",para = list(mean=1,sd=2))
za.test(x,"weibull",para = list(shape=1,scale=2))
za.test(x,"gamma",para = list(shape=2,scale=1))
za.test(x,"t",para = list(df=3))

perform a one- or two-sample analogue ZC of the Cramer-von Mises statistic

Description

The new statistics ZC appear similar to the Cramer-von Mises statistic, but it's generally much more powerful,see Jin Zhang(2002).

Usage

zc.test(x, y, para = NULL, N = 1000)
zc.test(x, y, para = NULL, N = 1000)

Arguments

`x`	a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed.
`y`	When tested as a single sample, a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. When tested as two-sample, a character string indicating what type of test was performed. Distributions "unif", "exponential", "normal", "lognormal", "gamma","t" and "weibull" are recognised.Here,the names of "exponential", "normal" and "lognormal" are simplified as "exp" ,"norm" and "lognorm" respectively.
`para`	A named list giving the parameters of the distribution specified and this can be omitted.
`N`	The number of replications in Monte Carlo simulation.The default value is 1000

Details

The ZC test is an EDF omnibus test for the composite hypothesis of distribution. The test statistic is

$Zc = \sum_{i=1}^{n}[\ln\frac{F_{0}(X_{(i)})^{-1}-1}{(n-0.5)/(i-0.75)-1}],$

Value

A list with class “htest” containing the following components:

`statistic`	the value of the ZC statistic.
`p.value`	the p-value for the test.
`method`	the character string “ZC test for given distribution”.
`data.name`	a character string giving the name(s) of the data.

Note

The ZC test is the recommended EDF test by Jin Zhang.

Author(s)

Ning Cui

References

Jin Zhang: Goodness-of-Fit Tests Based on the Likelihood Ratio.Journal of the Royal Statistical Society,64,281-294.

Jin Zhang,Yuehua Wu: Likelihood-ratio tests for normality.Computational Statistics & Data Analysis,49,709-721.

Jin Zhang: Powerful Two-Sample Tests Based on the Likelihood Ratio. Technometrics, 48:1, 95-103.

Examples

x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
zc.test(x,y)
zc.test(x,"unif")
zc.test(x,"norm")
zc.test(x,"unif",para = list(min=1,max=2))
zc.test(x,"exp",para = list(rate=1))
zc.test(x,"norm",para = list(mean=1,sd=2))
zc.test(x,"lognorm",para = list(mean=1,sd=2))
zc.test(x,"weibull",para = list(shape=1,scale=2))
zc.test(x,"gamma",para = list(shape=2,scale=1))
zc.test(x,"t",para = list(df=3))
x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
zc.test(x,y)
zc.test(x,"unif")
zc.test(x,"norm")
zc.test(x,"unif",para = list(min=1,max=2))
zc.test(x,"exp",para = list(rate=1))
zc.test(x,"norm",para = list(mean=1,sd=2))
zc.test(x,"lognorm",para = list(mean=1,sd=2))
zc.test(x,"weibull",para = list(shape=1,scale=2))
zc.test(x,"gamma",para = list(shape=2,scale=1))
zc.test(x,"t",para = list(df=3))

The analogue ZK of the Kolmogorov-Smirnov statistic

Description

The new statistics ZK appear similar to the Kolmogorov-Smirnov statistic, but it's generally much more powerful,see Jin Zhang(2002).

Usage

zk.test(x, y, para = NULL, N = 1000)
zk.test(x, y, para = NULL, N = 1000)

Arguments

`x`	a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed.
`y`	When tested as a single sample, a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. When tested as two-sample, a character string indicating what type of test was performed. Distributions "unif", "exponential", "normal", "lognormal", "gamma","t" and "weibull" are recognised.Here,the names of "exponential", "normal" and "lognormal" are simplified as "exp" ,"norm" and "lognorm" respectively.
`para`	A named list giving the parameters of the distribution specified and this can be omitted.
`N`	The number of replications in Monte Carlo simulation.The default value is 1000

Details

The Zk test is an EDF omnibus test for the composite hypothesis of distribution. The test statistic is

$Z_{k}=\max \limits_{1 \leq i \leq n}\{(i-0.5)\ln\frac{i-0.5}{nF_{0}(X_{(i)})}+(n-i+0.5)\ln\frac{n-i+0.5}{n[1-F_0(X_{(i)})]}\},$

Value

A list with class “htest” containing the following components:

`statistic`	the value of the ZK statistic.
`p.value`	the p-value for the test.
`method`	the character string “ZK test for given distribution”.
`data.name`	a character string giving the name(s) of the data.

Note

The Zk test is the recommended EDF test by Jin Zhang.

Author(s)

Ning Cui

References

Jin Zhang: Goodness-of-Fit Tests Based on the Likelihood Ratio.Journal of the Royal Statistical Society,64,281-294.

Jin Zhang,Yuehua Wu: Likelihood-ratio tests for normality.Computational Statistics & Data Analysis,49,709-721.

Jin Zhang: Powerful Two-Sample Tests Based on the Likelihood Ratio. Technometrics, 48:1, 95-103.

Examples

x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
zk.test(x,y)
zk.test(x,"unif")
zk.test(x,"norm")
zk.test(x,"unif",para = list(min=1,max=2))
zk.test(x,"exp",para = list(rate=1))
zk.test(x,"norm",para = list(mean=1,sd=2))
zk.test(x,"lognorm",para = list(mean=1,sd=2))
zk.test(x,"weibull",para = list(shape=1,scale=2))
zk.test(x,"gamma",para = list(shape=2,scale=1))
zk.test(x,"t",para = list(df=3))
x<-rbeta(50,shape1 = 0.6,shape2 = 0.8)
y<-rnorm(50)
zk.test(x,y)
zk.test(x,"unif")
zk.test(x,"norm")
zk.test(x,"unif",para = list(min=1,max=2))
zk.test(x,"exp",para = list(rate=1))
zk.test(x,"norm",para = list(mean=1,sd=2))
zk.test(x,"lognorm",para = list(mean=1,sd=2))
zk.test(x,"weibull",para = list(shape=1,scale=2))
zk.test(x,"gamma",para = list(shape=2,scale=1))
zk.test(x,"t",para = list(df=3))

Package 'DistributionTest'

Help Index

perform a one- or two-sample analogue ZA of Anderson-Darling statistic

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

perform a one- or two-sample analogue ZC of the Cramer-von Mises statistic

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

The analogue ZK of the Kolmogorov-Smirnov statistic

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples