lmomco (version 2.4.14)

quasmd: 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)

Value

Quantile value for nonexceedance probability \(F\).

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.

Author

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., tools:::Rd_expr_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, tools:::Rd_expr_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