For normal random variables
, X can be transformed into standard normal random variables
u through a linear transformation, as follows:
A normal or non-normal random variable Z can be approximated using one-dimensional Hermite orthogonal polynomials [[PSI].sub.i] of the standard normal random variables
[xi] as [17,18]
where [[alpha].sub.j] = [m.sub.j]/(1 + [b.sup.2.sub.j]), [[beta].sup.2.sub.j] = 2[[psi].sup.-1.sub.j] - 1 + 2[square root of [[psi].sup.-1.sub.j]] [square root of 2[[psi].sup.-1.sub.j] - 1], and [Z.sub.Vj] are independent standard normal random variables
In order to measure the (in)efficiency of Parliament in Asian countries, in this paper we propose a stochastic frontier production function for unbalanced panel data  assumed to be distributed as a half normal random variables
. This type of frontier and the computation method present advantages with respect other alternatives, for example the deterministic frontiers [12,16].
zero-mean normal random variables
x , y , and z with standard deviation [[sigma].sub.xyz] so that the new position of the receiver is now at coordinates (D + x',y',z').
For all scenarios, we assume that the bivariate normal random variables
(X, Y) have population parameters [[mu].sub.x] = 0, [[sigma].sub.x.sup.2] = [[sigma].sub.y.sup.2] = 1.
are normal random variables
with mean zero and covariance structure :
To view this issue from a different perspective, a chi-squared random variable with n degrees of freedom arises from summing the squares of n independent normal random variables
. Hence, a chi-squared random variable with 1 degree of freedom is simply the square of a normal random variable
where Z = [([Z.sub.1], ..., [Z.sub.m]).sup.T] is a random vector consisting of m mutually independent standard Normal random variables
, A is an n x m matrix, [mu] is an n x 1 vector and [??] stands for "equality in distribution." The relationship between [SIGMA] and A is given by [SIGMA] = [AA.sup.T].
randn for normal random variables
, and rand for continuous uniform