For a normally distributed population the quality of a given population sample can be assessed by comparing the sample frequency distribution to the normal distribution function.
We then combined P values for each gene across studies using the R function: (2) where x represents the vector of P values, pnorm is the normal distribution function, and qnorm is the normal quantile function.
For example, Nixon and Thompson [5] applied identity link functions both for gamma distribution of the costs and for the normal distribution of the effectiveness.
For instance, in the Normal distribution, θ=.
For the normal kernel function, the bandwidth is the standard deviation of the normal distribution.
For α=0, the skew normal distribution reduces to the normal distribution.
The lack of an analytical solution is caused by the fact that the relevant probability distributions, such as the normal distribution or Levy alpha-stable distributions have no closed form solutions for the cumulative distribution functions.
where MVN stands for multivariate normal distribution and Ψ denotes the digamma function.
almost surely, where stands for the standard normal distribution function, and,.
almost surely for all, where is the indicator function of the event and stands for the standard normal distribution function.
almost surely for all, here and in the sequel, is the indicator function of the event, and stands for the standard normal distribution function.
