lmomco (version 2.3.1)

cdflap: Cumulative Distribution Function of the Laplace Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Laplace distribution given parameters (\(\xi\) and \(\alpha\)) computed by parlap. The cumulative distribution function is $$F(x) = \frac{1}{2} \mathrm{exp}((x-\xi)/\alpha) \mbox{ for } x \le \xi \mbox{,}$$ and $$F(x) = 1 - \frac{1}{2} \mathrm{exp}(-(x-\xi)/\alpha) \mbox{ for } x > \xi \mbox{,}$$ where \(F(x)\) is the nonexceedance probability for quantile \(x\), \(\xi\) is a location parameter, and \(\alpha\) is a scale parameter.

Usage

cdflap(x, para)

Arguments

x

A real value vector.

para

The parameters from parlap or vec2par.

Value

Nonexceedance probability (\(F\)) for \(x\).

References

Hosking, J.R.M., 1986, The theory of probability weighted moments: IBM Research Report RC12210, T.J. Watson Research Center, Yorktown Heights, New York.

See Also

pdflap, qualap, lmomlap, parlap

Examples

# NOT RUN {
  lmr <- lmoms(c(123,34,4,654,37,78))
  cdflap(50,parlap(lmr))
# }