These distributions have been studied by some authors in recent years, as for example, Mudholkar and Srivastava (1993) for exponentiated Weibull, Gupta and Kundu (1999) for exponentiated exponential
, among others.
Caption: FIGURE 5: (a) Stem biomass per hectare in 72 months per vital area of the treatments and graphical representation of the Exponential
model adjusted; (b) Distribution of the residues for the stem biomass per hectare based on the spacing adjusted with the Exponential
model, at 72 months; (c) Stem biomass per hectare in 72 months per vital area of the treatments and graphical representation of the Hyperbolic model adjusted; (d) Distribution of the residues for the stem biomass per hectare based on the spacing adjusted with the Hyperbolic model, at 72 months.
Later, Jiang presented two nonlinear companding techniques, namely exponential
companding (EC)  and error companding (ErC) , to overcome the problem of increasing average power and to have efficient PAPR reduction.
The following section discusses weak exponentials
, and describes a condition for when weak exponentials
are given by tensor.
In , the autocorrelation function (ACF) of a wide-sense stationary (WSS) or short-range dependent process is modeled as a decaying exponential
A biexponential fit deviates systematically from the experimental data, but a triexponential fit is sufficiently flexible to describe adequately the data; further exponentials
result in ample uncertainties.
In their implementation, the first integral is roughly approximated by the left-rectangle numerical integration formula, and the matrix exponentials
are computed by a Crank-Nicolson type method.
Prony method is a technique for modeling time series data as a linear combination of exponentials
and it extends Fourier analysis.
and the subsequent developments of the concepts of geometry, the measure of time, mathematical operations (arithmetic, algebraic, exponentials
It allows execution of calculations with very long numbers, displaying them correctly without incomprehensible exponentials
so that frequencies are bounded by exponentials
with different arguments, in contrast to equation (6).
In this case the rise and decay curves are explained with the help of multiple component exponentials