Let G(x;ξ) be a baseline cumulative distribution function (cdf) and ξ be the vector of associated parameters.
For any baseline cumulative distribution function (cdf) G x), and (x in mathbb {R}), they defined the gamma-G family by the probability density function (pdf) f(x) and cdf F x) (for c>0) given by begin{array}rcl@ f(x)=frac{1}{Gamma c)},left{-log[1-G x)]right}^{c-1},left{-log[1-G x (1).
Examples are shown for diffusion T2 distribution functions and T1−T2 distribution functions.
For any baseline cumulative distribution function (cdf) G(x;η) (for (x in mathbb {R})) and probability density function (pdf) g(x;η)=d G(x;η)/d x, depending on a parameter vector η, let q denote the dimension of the vector η.
This would serve to essentially flatten the distribution of the baseline function and eliminate the foveal bias.
The first approach of generalization was suggested by Marshall and Olkin (1997) by adding one parameter to the survival function (overline {G}(x)=1-G x)), where G(x) is the cumulative distribution function (cdf) of the baseline distribution.
The joint distribution of Z(1) and Z(2) is defined by: It is assumed that the hazard function of subject i with and is given by (1) where λ0 t) is an arbitrary unspecified baseline hazard function, and α and γ are unknown regression coefficients.
According to [25], Weibull distribution function could be adopted as baseline function, as shown in (5).
Whether the actual number of flocks significantly exceeded the expected number was determined using a Poisson distribution for the variance of the baseline number, a continuity correction and the exact value for the Poisson distribution function in Excel 2000.
Whether these numbers significantly exceeded the expected numbers was determined looking at the upper 95% confidence level for the expected number assuming a Poisson distribution for the variance of the expected baseline number, a continuity correction, and the exact value for the Poisson distribution function in Excel 2000 [ 6].
