PBC_Z: Estimation of the p-value using linear regression with...
In genostats/tail.modeling: Estimation of small p-values

Description Usage Arguments Details Value Author(s) Examples

Estimates the p-value of a data set z for a test statistic Zobs with the Box-Cox function.

1	PBC_Z(z,Ntot,N,param,Zobs,draw)

`z`	Data set resulting from the initial one- sorted list of real numbers
`Ntot`	Number of observations in the initial data set - integer
`N`	Number of observations in the data set z - integer
`param`	Box-cox parameter lambda - real number: if param is missing, the parameter will be estimated with least squares; if it is a real number, this value will be used for lambda without performing any estimation
`Zobs`	Test statistic of the data set - real number
`draw`	If the linear regression of the Box-Plot method should be plotted or not - Boolean.

The method is to compute the coefficients of the linear regression between log(-log(p)) and BoxCox(log(z)) where p is a list of probabilities correspondings to the sorted list of test statistics z.

Returns a list composed of:

`p`	The value of the estimated p-value - real number
`interc`	The intercept of the linear regression used to estimate the p-value - real number
`pente`	The slope of the linear regression used to estimate the p-value - real number
`lbda`	The estimated parameter lambda (or the lambda given if not estimated) - real number

Marion

PBC_Z(z = tail(sort(rnorm(1e6)),500),Ntot = 1e6,N = 500,Zobs = 3)

## The function is currently defined as
function(z,Ntot,N,param,Zobs,draw){
  p<-seq(N,1)/Ntot
  if (missing(param))
    lambda <- BoxCox_lm(log(-log(p)),log(z))
  else
    lambda <- param
  coeffs <- lm(  log(-log(p)) ~ BoxCox(log(z),lambda) )$coefficients
  if (draw == TRUE)
    plot(coeffs[[1]] + BoxCox(log(z),lambda) * coeffs[[2]],log(-log(p)),col="red",main="Linear regression of the Box-Plot method")
  return(list(p = exp(-exp(sum( coeffs*c(1, BoxCox(log(Zobs),lambda))))),
              interc = coeffs[[1]],
              pente = coeffs[[2]],
              lbda = lambda))

}