![]() ![]() Consider, however, if three absences make a suspension, then aren't two absences equal to 0. ![]() ![]() Counts are usually considered exact and integer. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together. Quantum Mechanics, the field of physics which deals with the very small, is much concerned with discrete values.Īnother example might be how many students were absent on a given day. In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. is possible, but 1.5 children are not meaningful.Ĭredit card number: The number is a discrete value, but cannot be used for addition or subtraction, etc.Īnother classic is the spin or electric charge of a single electron. The number of children someone has: 1, 2, 3, etc. These are commonly used on arbitrary scales, such as scoring your level of happiness, although such scales can also be continuous.ĭiscrete data can be used as ordered categorical data in statistical analysis, but some information is lost in doing so. In some situations, mathematical functions or calculations are not possible either.ĭiscrete variables are measured across a set of fixed values, such as age in years (not microseconds). A specific number of isolated values are anticipated in discrete data, unlike continuous data, which is tied to physical measurement and expects any value from. "Stability for random measures, point processes and discrete semigroups." Bernoulli 17 (3) 1015 - 1043, August 2011.Discrete data arise from observations that can only take certain numerical values. Particular examples include discrete stable vectors that generalise discrete stable random variables and the family of natural numbers with the multiplication operation, where the primes form the basis. For a probability measure on 0, 1 without discrete component, the best possible order of approximation by a finite point set in terms of the. The obtained results are then applied to explore stable random elements in discrete semigroups, where the scaling is defined by means of thinning of a point process on the basis of the semigroup. An alternative cluster representation for such processes is also derived using the so-called Sibuya point processes, which constitute a new family of purely random point processes. Most classical, combinatorial probability models are based on underlying discrete uniform distributions. The distribution corresponds to picking an element of S at random. As a consequence, spectral representations are obtained for the probability generating functional and void probabilities of discrete stable processes. The discrete uniform distribution is a special case of the general uniform distribution with respect to a measure, in this case counting measure. We give spectral and LePage representations for general strictly stable random measures without assuming their independent scattering. It is shown that these processes are exactly Cox (doubly stochastic Poisson) processes with strictly stable random intensity measures. In a nutshell, discrete variables are points plotted on a chart and a continuous variable can be plotted as a line. Similarly defining the scaling operation as thinning of counting measures we characterise the corresponding discrete stability property of point processes. Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. ![]()
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