Is this the correct closed form estimation of Gamma Process mean & variance rates from data?

Is this the correct closed form estimation of Gamma Process mean &
variance rates from data?

I cannot find a single paper that details how to determine the mean and
variance rates of a Gamma Process from data; however, wikipedia has a few
closed forms, and the reason I ask is because I'm confused with the usages
of some terms and unfamiliar with their definitions & identities.
Wikipedia's Gamma Process page says
The gamma process is sometimes also parameterised in terms of the mean
($\mu$) and variance ($v$) of the increase per unit time, which is
equivalent to $\gamma=\mu^2/v$ and $\lambda=\mu/v$
and
The marginal distribution of a gamma process at time $t$, is a gamma
distribution with mean $\gamma t/\lambda$ and variance $\gamma
t/\lambda^2$.
Wikipedia's Variance Distribution page says the mean and variance is
$$E[X]=k\theta$$ $$Var[X]=k\theta^2$$
It also gives estimations for shape and scale
$$\hat\theta={1\over{kN}}\sum\limits_{i=1}^N x_i$$
$$s=ln({1\over N}\sum\limits_{i=1}^N x_i)-{1\over N}\sum\limits_{i=1}^N
ln(x_i)$$
$$k\approx{{3-s+\sqrt{(s-3)^3+24s}}\over{12s}}$$
Is it correct to that the "mean (ì) and variance (v) of the increase per
unit time" are the "mean and variance rates" of a Gamma Process? If so, is
it correct to solve for $\mu$ and $v$ by
Calculating the shape and scale parameters of the Gamma Distribution from
data then
Calculate the mean and variance of the Gamma Distribution from the shape
and scale parameters of the Gamma Distribution then
Solve for $\gamma$ and $\lambda$ by simultaneous equations from the mean
and variance of the Gamma Distribution with $t$ from data and calculate
their results, finally
Solve for mean ($\mu$) rate and variance ($v$) rate of the Gamma Process
by simultaneous equations from $\lambda$ and $\gamma$ of the Gamma
Distribution and calculate their results
?