Mean and variance of exponential and gamma distributions

[lgawarec]

The mean and variance displayed are incorrect. For example
visualize.exp(1,theta=2,"lower")
pexp(1,rate=2)

give the same probabilities, but mu=2 and sigma^2=4 are displayed instead of mu = 0.5 and sigma^2=0.25.

[coatless]

@lgawarec Mmm, there might be a hang up in how the exponential distributions are implemented.

If we're using R's implementation, this rests upon:

$$f(w) = \lambda e^{-\lambda w}$$

However, visualize.exp() function signature is noting a $\theta$ parameterization:

$$f(x) = \frac{1}{\theta} e^{-x/\theta}$$

Though, glancing at the source:

visualize/R/visualize.exp.R

Lines 33 to 35 in c43b25c

	function(stat = 1, theta = 1, section = "lower") {
	visualize.it('exp', stat = stat, list(theta = theta), section = section)
	}

We're directly using R's implementation.

So, we'll need to apply a conversion between the two of a quick division:

$\theta=\frac{1}{\lambda}$ and $\lambda=\frac{1}{\theta}$

Thanks for finding the bug!