Table 1: Survey of contributions to quantile approximation

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).

 



 

 

 

 

 

 

 

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)