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A function whose integral from A to B (with A less than or equal to B) gives the probability that a corresponding random variable assumes a value on the interval from A to B. Probabilities are given by appropriate areas under the curve representing this function.
For a continuous random variable X, the probability of X lying in a particular interval is found by integrating the p.d.f., f(x) over that interval. The p.d.f. is usually obtained by assuming a theoretical distribution for X. Note that the total area under the curve of f(x) is 1, and the function is always positive.
pdf) A mathematical model that describes the probability of events occurring over time. This function is integrated to obtain the probability that the event time takes a value in a given time interval. In life data analysis, the event in question is a failure, and the pdf is the basis for other important reliability functions, including the reliability function, the failure rate function and the mean life.
The function that describes the change of certain realizations for a continuous random variable.
Consider an uncertain physical property and a corresponding space describing the range of values that the property can have (e.g., the configuration of a thermally excited particle system and the corresponding 3 dimensional configuration space). The probability density function associated with a property is defined over the corresponding space; its value at a particular point is the probability per unit volume that the property has a value in an infinitesimal region around that point.
A function associated with a continuous random variable such that the probability of the r.v. falling in an interval is given by the area lying between the graph of the function and the -axis and bounded by the ends of the interval.
Associated with a random variable is a probability density function (pdf). For continuous random variables this has the property that for any interval on the real line, the probability of the random variable realising a value in the interval is given by the integral of the pdf over this interval. (The integral of a pdf over the entire real line is always unity).
A function that gives the likelihood that a random variable has values in the set. Weight vectors get stuck in isolated regions in Kohonen and counter propagation networks. This can be prevented by adding noise to the data, which makes the probability density function positive everywhere. This works, but it is slower than convex combination.
Used to generate a random sequence of events conforming to a given mean value and frequency distribution.