Quantile mechanics: Issues arising from critical review

Table 2: Authors contribution to the QM approach of quantile approximation of different distributions

Distribution	Authors
Beta	Steinbrecher and Shaw (2008)
Exponential	Shaw et al. (2014), Shaw and Brickman (2009)
Gamma	Steinbrecher and Shaw (2008), Luu (2016, 2015)
Generalized inverse Gaussian	Munir (2013), Munir and Shaw (2012)
Hyperbolic	Munir (2013), Shaw et al. (2014), Shaw and Brickman (2009), Munir and Shaw (2012)
Non-central chi square	Munir (2013)
Normal	Steinbrecher and Shaw (2008), Luu (2016), Shaw et al. (2014), Shaw and Brickman (2009), Shaw and McCabe (2009), Alu (2011)
Skew-normal	Luu (2016)
Snedecor’s F	Munir (2013)
Student’s t	Steinbrecher and Shaw (2008), Shaw et al. (2014), Shaw and Brickman (2009), Shaw and McCabe (2009)
Symmetric generalized Hyperbolic	Shaw and McCabe (2009)
Variance gamma	Munir (2013), Shaw et al. (2014), Shaw and Brickman (2009), Munir and Shaw (2012)
α stable	Munir (2013), Munir and Shaw (2012)
Some selected convoluted distributions	Okagbue et al. (2018)

Distribution	Details
Chi-square	Lin (1994), Ittrich et al. (2000).
Beta	Thomson (1947), Gil et al. (2017).
Behrens-Fisher	Patil (1969), Davis and Scott (1973).
F	Abernathy and Smith (1993a, b), Torigoe (2011).
Gamma	Withers and Nadarajah (2014), Gil et al. (2015).
Nakagami	Bilim and Develi (2015), Kabalci (2018).
Non-central chi-square	Torigoe (1996), Sahai and Ojeda (2009).
Non-central student t	Akahira (1995), Sahai and Ojeda (1998).
Normal (probit)	Odeh and Evans (1974), Beasley and Springer (1977), Wichura (1987, 1988), Lin (1990), Acklam (2003), Soranzo and Epure (2014).
Pearson(general)	Bowman and Shenton (1979).
Student t	Shaw (2006), Schluter and Fischer (2012).