For the probabilities to sum to 1, divide exp(xβ m ) by (mathop sum limits_{j = 1}^{J} { exp }({x}_{i}{beta}_{j} ).) Although the probability sum is 1, the set of parameters that generate the probabilities is not identified since more than one set of parameters can generate the same probabilities.
For the probabilities P DL and P DP the explicit formula to compute the corresponding probabilities could also be included within the paragraph analogous to P RF.
To ensure nonnegativity for the probabilities, the exponential of xβ m is used.
For some special values of p, Σ1 and Σ2 we obtain explicit formulas and inequalities for the probabilities of misclassification.
where w s,w c, and w t are weights for the probabilities of success, collision, and timeout, respectively.
I present predictive results for the probabilities of purchasing secondary housing, an automobile, and other big ticket items.
In some situations there are no frequencies available to use as estimates for the probabilities, or it might be practically impossible to obtain those frequencies.
We provide closed-form expressions for the probabilities in Wei's [1997. A class of designs for requential clinical trials. J. Amer. Statist. Assoc.
Two adaptive detectors, i.e., generalized likelihood ratio and adaptive matched filter, are then adopted, and their expressions for the probabilities of false alarm and detection are provided.
It is important that proper estimates are made for the probabilities of the occurrence of failures, as well as for their effects.
Before the numerical analysis, we first provide expressions for the probabilities of operating in each one of the four scenarios described in "State transition model" section.
