cdflmrq {lmomco}

Cumulative Distribution Function of the Linear Mean Residual Quantile Function Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the “Linear Mean Residual Quantile Function” distribution given parameters computed by parlmrq. The cumulative distribution function has no explicit form and requires numerical methods. The R function uniroot is used to root the quantile function qualmrq to compute the nonexceedance probability. The function returns 0 or 1 if the x argument is at or beyond the limits of the distribution as specified by the parameters. The cdflmrq function is also used with numerical methods to solve the pdflmrq.

Usage

cdflmrq(x, para, paracheck=FALSE)

Arguments

x

A real value vector.

para

The parameters from parlmrq or vec2par.

paracheck

A logical switch as to whether the validity of the parameters should be checked. Default is paracheck=TRUE. This switch is made so that the root solution needed for cdflmrq exhibits an extreme speed increase because of the repeated calls to qualmrq.

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

References

Midhu, N.N., Sankaran, P.G., and Nair, N.U., 2013, A class of distributions with linear mean residual quantile function and it's generalizations: Statistical Methodology, v. 15, pp. 1–24.

See Also

pdflmrq, qualmrq, lmomlmrq, parlmrq

Examples

  lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2))
  cdflmrq(2,parlmrq(lmr))