This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with speci c properties, and that every function with these speci c properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized b...

although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. by the way there is an urgent need to find a method to foresee this catastrophic event. there are a lot of methods for forecasting the time of earthquake occurrence. another method for predicting that is to know probability density function of time interval between earth...

in this paper, we propose and study exp-kumaraswamy distribution. some of its properties  are derived, including the density function, hazard rate function, quantile function, moments,  skewness  and kurtosis.   adata set isused to illustrate an application of the proposed distribution. also, we obtain a new distribution by transformation onexp-kumaraswamy distribution.   new distribution is an...

The gap probability generating function has as its coefficients the probability of an interval containing exactly k eigenvalues. For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the gap probability generating functions have the special property that they can be evaluated in terms of Painlevé transcendents. The derivation of these results m...

Since the emergence of power market, the target of power generating utilities has mainly switched from cost minimization to revenue maximization. They dispatch their power energy generation units in the uncertain environment of power market. As a result, multi-stage stochastic programming has been applied widely by many power generating agents as a suitable tool for dealing with self-scheduling...

The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random v...