# Student's distribution - Schweser Secret Sauce is wrong !

Don’t get me wrong, the Secret Sauce is great. There are just a few points to correct (and may be a few additional information to provide). p33 of the SS, you will find a graphical illustration of the Student’s t-distribution. This illustration is wrong because when the degrees of freedom increase the Student distribution is supposed to converge toward the normal distribution (please see Wikipedia: http://en.wikipedia.org/wiki/Student’s_t-distribution ). In the SS, the illustration shows that the distribution become more peaked when df increases. I already informed Schweser of this error. Schweser agree that this is erroneous but it seems that this is the way it is presented in the CFAI’s reading and because of that they haven’t issued an errata on that issue. Here again, my point is to say that the errors should be corrected… Marc

sigh…

If you don’t trust schweser & CFAI, perhaps you should have another looky at that link you posted. Specifically the chart on the right showing the PDF. There is nothing to correct.

CFAI also says rivers flows downhill… wtf???

Seems to me that perhaps one might want to start reading the material prior to studying the secret sauce…especially when the test is practically 6 months away…That way, questions like this won’t come up.

Guys, I don’t understand your aggressivity. If you don’t find it erroneous, then talk to a mathematician, an actuary or any quant so that they explain you why it is not *perfectly* correct. Do you need to understand that to pass the Level 1? Of course you don’t as many things. But if you want to make progress, to understand things in depth, then may be you should think it twice. Regards, Marc

I think you need to start by looking at the fact that many esteemed members of this board are telling you you’re wrong in many of your points. Maybe you should rethink your gameplan.

hm… with greater df the distribution becomes “normal” so its peak is increasing as it approaches infinity. Aint that right? Thats what Schweser taught me.

ancientmtk, Yes, with greater df, the t-distibution converges toward the normal distribution. The illustration shows the normal distribution in bold. Then there are a few t-distributions for various df, all having a peak higher than the normal, which is not correct. In addition the t-distributions don’t seem to converge toward the normal distribution. I haven’t checked the reading but, according to Schweser, CFAI posted an errata regarding the peakedness of the t-distribution. So the reading must be wrong as well. black swan, A charter holder or any contributor may know a lot of things, there may still be a lot of things he does not know and among those a few that I know. Isn’t it the purpose of this forum: try to help each others and make progresses together? So far, I don’t see many points where I’m wrong - which does not mean I’m always right. Regards, Marc

If you want to contemplate that picture a little you can think about how the kind of convergence they are showing relates to converge in distribution like in the central limit theorem (it’s much stronger)

joeydvivre, The central limit theorem (or the weak law of large number) gives the convergence in law. What do you mean by “it’s much stronger”? All I’m saying is that this picture does not show the convergence in law as it should. But haven’t you said that you don’t have the SS? So how can you see the picture? Regards, Marc

I haven’t seen the pictures, but the pictures should look like a bunch of bell-shaped curves with the top of the bell increasing with df until it looks more and more like a normal pdf. But that’s not any kind of probabilistic convergence; it’s uniform convergence (in the sense of calculus) of density functions.

It should be as you describe and it is. But in addition, and this is what is not correct, as df increases the t-distribution should converge toward the normal distribution. There are different types of convergence used in statistics: “convergence in distribution” or “in law”, the “convergence in probability”, the “almost sure convergence” and the “sure convergence”. The central theorem does not grant the “uniform convergence” but only the “convergence in law” which is weaker. I haven’t checked it, I’m pretty sure the t-distribution does NOT converges uniformely toward the normal distribution. The t-distribution converges *in law* toward the normal distribution. This is what is missing in the diagram. Regards, Marc

That’ll be a chap with a PhD in statistics you are debating with.

Dude, I love this. Keep up the good posts.

mhannebert Wrote: ------------------------------------------------------- > It should be as you describe and it is. But in > addition, and this is what is not correct, as df > increases the t-distribution should converge > toward the normal distribution. > > > There are different types of convergence used in > statistics: “convergence in distribution” or “in > law”, the “convergence in probability”, the > “almost sure convergence” and the “sure > convergence”. > The central theorem does not grant the “uniform > convergence” but only the “convergence in law” > which is weaker. I haven’t checked it, I’m pretty > sure the t-distribution does NOT converges > uniformely toward the normal distribution. > > The t-distribution converges *in law* toward the > normal distribution. > This is what is missing in the diagram. > > Regards, > > Marc Convergence in probability says nothing about density functions. In fact, density functions don’t even need to exist. But here the T-distribution pdfs certainly converge uniformly to the normal (the biggest diff is at 0, right?). It doesn’t make sense to say that a t-distribution converges in law to a normal, thought it would make sense to say that a sequence of T r.v.'s with increasing df converges in law to a normal.