Context . Statistical properties of the cosmic density fields are to a large extent encoded in shape one-point probability distribution functions (PDF) as measured surveys. In order successfully exploit such observables, detailed functional form covariance matrix PDF is needed. Aims The objectives model this for general stochastic and that reproduce expected cosmology. accuracy proposed forms e...

Probability density function methods for characterizing various fluctuating quantities in the reacting gas phase of turbulent spray flames are presented, development which O'Brien has been a pioneer. Balance equations two-phase flows considered as piecewise continuous medium first presented with interface conditions containing vaporization–condensation equilibrium. From these, equation joint pr...

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead best prediction result. In study, numerical simulations conducted using that follow normal and we examine whether functions have shapes different from can yield larger log-likelihoods than in light future data. The results indicate fitting prod...