A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.

Continuous A continuous bivariate joint density function defines the probability distribution for a pair of random variables. For example, the function f (x,y) = 1 when both x and y are in the ...

Example of the Hazard Rate The probability density calculates the probability of failure at any given time. For instance, a person is certain to die eventually.

Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for ...

In some situations only the statistical properties of such objects are desired: the three-dimensional probability density function. This article demonstrates that under special symmetries this ...

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Based upon ...