Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and...

Two real-valued or vector-valued random variables X, Y are independent for probability measure P (written: X ⊥ Y [P ]) if for all sets A and B, P[X ∈ A, Y ∈ B] = P[X ∈ A] · P[Y ∈ B]. For jointly discrete or jointly continuous random variables this is equivalent to factoring of the joint probability mass function or probability density function, respectively. The variables X and Y are conditiona...

The estimation of P(Sn > u) by simulation, where Sn is the sum of independent, identically distributed random varibles Y1, . . . , Yn, is of importance inmany applications. We propose two simulation estimators based upon the identity P(Sn > u) = nP(Sn > u, Mn = Yn), where Mn = max(Y1, . . . , Yn). One estimator uses importance sampling (for Yn only), and the other uses conditional Monte Carlo c...

In this paper we introduce the class of Wp scale mixture random vectors with a particular radial decomposition and a independent splitting property specified by some random variable Wp, p ∈ (0,∞). We derive several conditional limit results assuming that the distribution of the random radius is in the max-domain of attraction of a univariate extreme value distribution andWp has a certain tail a...