truncated Normal moments

Posted in Books, Kids, Statistics with tags , , , , , on May 24, 2019 by xi'an

An interesting if presumably hopeless question spotted on X validated: a lower-truncated Normal distribution is parameterised by its location, scale, and truncation values, μ, σ, and α. There exist formulas to derive the mean and variance of the resulting distribution,  that is, when α=0,

$\Bbb{E}_{\mu,\sigma}[X]= \mu + \frac{\varphi(\mu/\sigma)}{1-\Phi(-\mu/\sigma)}\sigma$

and

$\text{var}_{\mu,\sigma}(X)=\sigma^2\left[1-\frac{\mu\varphi(\mu/\sigma)/\sigma}{1-\Phi(-\mu/\sigma)} -\left(\frac{\varphi(\mu/\sigma)}{1-\Phi(-\mu/\sigma)}\right)^2\right]$

but there is no easy way to choose (μ, σ) from these two quantities. Beyond numerical resolution of both equations. One of the issues is that ( μ, σ) is not a location-scale parameter for the truncated Normal distribution when α is fixed.

ABC in Sydney, July 3-4, 2014!!!

Posted in pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , on February 12, 2014 by xi'an

After ABC in Paris in 2009, ABC in London in 2011, and ABC in Roma last year, things are accelerating since there will be—as I just learned—  an ABC in Sydney next July (not June as I originally typed, thanks Robin!). The workshop on the current developments of ABC methodology thus leaves Europe to go down-under and to take advantage of the IMS Meeting in Sydney on July 7-10, 2014. Hopefully, “ABC in…” will continue its tour of European capitals in 2015! To keep up with an unbroken sequence of free workshops, Scott Sisson has managed to find support so that attendance is free of charge (free as in “no registration fee at all”!) but you do need to register as space is limited. While I would love to visit UNSW and Sydney once again and attend the workshop, I will not, getting ready for Cancún and our ABC short course there.