quasmd {lmomco}

Quantile Function of the Singh–Maddala Distribution

Description

This function computes the quantiles of the Singh–Maddala (Burr Type XII) distribution given parameters (\xi, a, b, and q) computed by parsmd. The quantile function is

x(F) = \xi + a\biggl((1-F)^{-1/q} - 1 \biggr)^{1/b}\mbox{,}

where x(F) with 0 \le x \le \infty is the quantile for nonexceedance probability F, \xi is a location parameter, a is a scale parameter (a > 0), b is a shape parameter (b > 0), and q is another shape parameter (q > 0).

Usage

quasmd(f, para, paracheck=TRUE)

Arguments

f

Nonexceedance probability (0 \le F \le 1).

para

The parameters from parsmd or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

Author(s)

W.H. Asquith

References

Kumar, D., 2017, The Singh–Maddala distribution—Properties and estimation: International Journal of System Assurance Engineering and Management, v. 8, no. S2, 15 p., doi:10.1007/s13198-017-0600-1.

Shahzad, M.N., and Zahid, A., 2013, Parameter estimation of Singh Maddala distribution by moments: International Journal of Advanced Statistics and Probability, v. 1, no. 3, pp. 121–131, doi:10.14419/ijasp.v1i3.1206.

See Also

cdfsmd, pdfsmd, lmomsmd, parsmd

Examples

quasmd(0.99, parsmd(vec2lmom(c(155, 118.6, 0.6, 0.45)))) # 1547.337 99th percentile