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

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 ...

Nonparametric methods provide a flexible framework for estimating the probability density function of random variables without imposing a strict parametric model. By relying directly on observed ...

Ushio Sumita, Yasushi Masuda, Classes of Probability Density Functions Having Laplace Transforms with Negative Zeros and Poles, Advances in Applied Probability, Vol. 19, No. 3 (Sep., 1987), pp.

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply ...

In this paper, we propose a functional linear regression model in the space of probability density functions. We treat a cross-sectional distribution of individual earnings as an infinite dimensional ...

Nonparametric method for multivariate density estimation using neural networks In this paper, a parameter-free method is proposed to determine the probability density function of multi-dimensional ...

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 ...

F (t) is the probability density function (PDF), or the probability that the value (failure or death) will fall in a specified interval, such as a specific year.