dinvgaussian function is incorrect

[samsemegne]

The dinvgaussian function, the pdf of the inverse-Gaussian distribution, produces incorrect results.

It doesn't integrate to 1 like a proper pdf, but to 1.732051. Its moments also mismatch what they should algebraically be, e.g. its expected value should equal the mu parameter, but it isn't.

I discovered the issue. Discord user Clarinetist#7695 identified the problem to be in this piece of code:

dens <- log(lambda/(2 * pi * x^3)^0.5) - ((lambda * (x - mu)^2)/(2 * mu^2 * x)) if (log == FALSE) dens <- exp(dens)

Stating: "Taking the log of this, it should be"
"$$\log f(x) = \dfrac{1}{2}\log\left(\dfrac{\lambda}{2\pi x^3} \right) - \dfrac{\lambda (x-\mu)^2}{2\mu^2 x}$$"

[singmann]

Can you submit a pull request please that fixes this?