FGPD: Pareto's cumulative distribution function
In genostats/tail.modeling: Estimation of small p-values

Description Usage Arguments Value Author(s) References Examples

Computes the value of the distribution function of Pareto. The method of parameters' estimation can be chosen.

1	FGPD(z,zexc,estim)

`z`	Real number in which the function will be evaluated - can also be a list of real numbers
`zexc`	Data set - sorted list of real numbers
`estim`	Method to estimate the parameters of Pareto's function - String: either "EMV" for the method of maximum likelihood or "PWM" for the method of probability weighted moments

Returns a list composed of:

`val`	The value of the cumulative distribution function evaluated in z using the method of estimation chosen - real number
`k`	The estimated parameter k of Pareto's cumulative distribution function - real number
`a`	The estimated parameter a of Pareto's cumulative distribution function - real number

Marion

Theo A. Knijnenburg, Lodewyk F. A. Wessels, Marcel J. T. Reinders and Ilya Shmulevich, Fewer permutations, more accurate P-values, Bioinformatics.

FGPD(30,sort(rnorm(1e6)),"PWM")

## The function is currently defined as
function (z, zexc, estim)
{
  if (estim == "EMV")
    coeff<-EMV(zexc)
  else
    coeff<-PWM(zexc)
  a<-coeff$a
  k<-coeff$k
  if (k!= 0)
    return(list(val = 1-(1-k*z/a)^(1/k),
                k = k,
                a = a))
  else
    return(list(val = 1-exp(-z/a),
                k = k,
                a = a))
  }