To solve for turbulent flow without closely associated defferent dynamical mechanics, a probability density function
method is adopted to describe the pulsating intensity of velocity of fluid particles in this study.
7) The iterative estimation process uses a golden section search  over a prespecified interval for k to maximize the Probability-Probability plot likelihood between the probability density function
of the collected data ([DELTA][lambda](k)) and the probability of the instrumental variable Z generated as
This model revealed three properties of growth: separability, self-similarity and a Gaussian branch density function
1 represents the variable of interest while P along the vertical axis represents the cumulated distribution function (CDF), which relates the probabilistic density function
(PDF) p(x) through [mathematical expression not reproducible].
For a given image X, the probability density function
The plots of the two density functions
show a difference in the means, as well as a slight difference in their scales.
The reverse Hazard rate function was determined as the relation among the probability density function
and it's confirming distribution function.
Differentiating H (x), we get the density function
of the gamma-[(1- Exp)/Exp] distribution:
The initial two moments of the Weibull density function
are used to conclude the parameters 'k' and 'c'.
In the paper titled "Outliers in Data Envelopment Analysis", Taylor Boyd, Grade Docken and John Ruggiero advance a method of estimating the production frontier in the presence of outliers using the stochastic DEA model of Banker (1988) with assumptions on the probability density function
of the inefficiency term.
As the probability density function
for the Dirichlet distribution is equal to
For example, Rivlin and Saunders  proposed that a strain energy density function
is expressible in the form of even powered series of the principal stretches.