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 ...

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 ...

D. O. Loftsgaarden, C. P. Quesenberry, A Nonparametric Estimate of a Multivariate Density Function, The Annals of Mathematical Statistics, Vol. 36, No. 3 (Jun., 1965 ...

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 ...

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.

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 ...