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Probability and Statistics
Published in Paul J. Fortier, George R. Desrochers, Modeling and Analysis of Local Area Networks, 1990
Paul J. Fortier, George R. Desrochers
The simplest of all probability distributions is the discrete uniform distribution. Such a distribution states that all values of the random variable are equally probable and depend only upon the number of possible outcomes of the experiment. The density function for the uniform distribution is given as () f(x)=1kx=x1,x2…xk
Choosing a Probability Distribution
Published in Charles Yoe, Principles of Risk Analysis, 2019
The discrete distribution (Figure 13.26), not to be confused with the distribution of a discrete random variable, is made up of a limited number of values or alternative outcomes (A, B, C in the figure). Each of these values/alternative outcomes, which need not be sequential, has a probability of occurring, and that probability can vary. The discrete uniform distribution is a special case of the discrete and is the discrete equivalent of the continuous uniform distribution. All integer values in the discrete uniform distribution are equally likely to occur. Its parameters include a number of x-values and the probability of each x-value.
Probability Distributions
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
The classic example of the Discrete Uniform Distribution is that of a conventional die. We have an equal chance (i.e. one in six) of throwing any integer number from one to six. An even simpler but also a classic example is that of tossing a coin which has only two possible outcomes, of equal probability, but neither of which are numeric.
Data-driven distributionally robust risk parity portfolio optimization
Published in Optimization Methods and Software, 2022
Our modelling framework provides sufficient flexibility for the user to prescribe their own choice of . However, given the data-driven nature of our manuscript, we formally define the nominal probability distribution as a discrete uniform distribution, i.e. . This falls in line with our goal to define the most adversarial distribution relative to the distribution implied by the data.