changepoint (version 0.3)

single.meanvar.gamma: Single Change in Mean and Variance - Gamma Data (i.e. change in scale parameter)

Description

Calculates the scaled log-likelihood (assuming the data is Gamma distributed) for all possible changepoint locations and returns the single most probable (max).

Usage

single.meanvar.gamma(data, shape=1, penalty="SIC",value=0,class=TRUE,param.estimates=TRUE)

Arguments

data

A vector or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset.

shape

Numerical value of the true shape parameter for the data. Either single value or vector of length nrow(data). If data is a matrix and shape is a single value, the same shape parameter is used for each row.

penalty

Choice of "None", "SIC", "BIC", "AIC", "Hannan-Quinn" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the value parameter.

value

The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint,

class

Logical. If TRUE then an object of class cpt is returned. If FALSE a vector is returned.

param.estimates

Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.

Value

• If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. The structure of cpts is as follows.

  If data is a vector (single dataset) then a single value is returned:

• cpt
  The most probable location of a changepoint if H0 was rejected or NA if H1 was rejected.
• If data is an mxn matrix (multiple datasets) then a vector is returned:
• cpt
  Vector of length m containing where each element is the result of the test for data[m,]. If cpt[m] is a number then it is the most probable location of a changepoint under H1. Otherwise cpt[m] has the value NA and indicates that H1 was rejected.

Details

This function is used to find a single change in scale parameter (mean and variance) for data that is assumed to be Gamma distributed. The value returned is the result of testing H0:no change in mean or variance against H1: single change in mean and/or variance using the log of the likelihood ratio statistic coupled with the penalty supplied.

References

Change in Gamma scale parameter: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser

See Also

cpt.meanvar,single.meanvar.norm,cpt

Examples

# Example of a change in scale parameter (mean and variance) at 100 in simulated gamma data
set.seed(1)
x=c(rgamma(100,shape=1,rate=1),rgamma(100,shape=1,rate=5))
single.meanvar.gamma(x,penalty="SIC",class=FALSE) # returns 97 to show that the null hypothesis was rejected and the change in scale parameter is at 97
ans=single.meanvar.gamma(x,penalty="AIC")
cpts(ans) # returns 97 to show that the null hypothesis was rejected, the change in scale parameter is at 97

# Example of a data matrix containing 2 rows, row 1 has a change in scale parameter and row 2 had no change in scale parameter
set.seed(10)
x=c(rgamma(100,shape=1,rate=1),rgamma(100,shape=1,rate=10))
y=rgamma(200,shape=1,rate=1)
z=rbind(x,y)
single.meanvar.gamma(z,penalty="SIC",class=FALSE) # returns vector c(99,200) which shows that the first dataset has a change in scale parameter at 99 and the second dataset rejected H1 and has no change in scale parameter
ans=single.meanvar.gamma(z,penalty="Manual",value="diffparam*log(n)") # list returned
cpts(ans[[1]]) # test using a manual penalty which is the same as the SIC penalty for this example.  The same changepoint is detected for the first dataset 
cpts(ans[[2]]) # same as above, no change found