Figure 1: Probability density plots of the AL ( γ = 0) and the GAL ( γ = 0) distributions. distribution can have tails which are heavier or narrower than the AL distribution. These characteristics make the GAL distribution more flexible than the AL distribution. Ordinal models arise when the dependent (response) variable is discrete and outcomes are inherently ordered or ranked such that the scores assigned to outcomes have an ordinal meaning, but no cardinal interpretation (Johnson and Albert, 2000; Jeliazkov and Rahman, 2012). For example, in a survey on public opinion to allow more offshore drilling, responses may be recorded as follows: 1 for ‘strongly oppose’, 2 for ‘somewhat oppose’, 3 for ‘somewhat support’ and 4 for ‘strongly support’ (Mukherjee and Rahman, 2016). The responses have ordinal meaning but no cardinal interpretation, so one cannot say that a score of 4 implies four times more support compared to a score of 1. We adopt the latent variable approach and represent the FBQROR model using a a continuous latent random variable z$_{i}$ expressed as a function of covariates and error as, 3. The FBQROR Model z$_{i}$ = x ′ $_{i}$β + ϵ$_{i}$, ∀ i = 1 , · · · , n, (7) 7 −10 0 10 20 0 0.02 0.04 0.06 0.08 0.1 0.12 f(y| , , ) p$_{0}$ = 0.10 =0 =−0.1 =3 =6 −10 −5 0 5 10 0 0.05 0.1 0.15 0.2 0.25 p$_{0}$ = 0.50 =0 =−0.7 =0.5 =0.9 −20 −10 0 10 0 0.02 0.04 0.06 0.08 0.1 0.12 p$_{0}$ = 0.90 =0 =−6 =−3 =0.1