Wikipedia:Reference desk/Archives/Mathematics/2008 May 25#variance of t-distribution

To give a bit of context, here is a payoff matrix (well not a matrix because I don't know how to do them) for the Hawk-Dove game

Hawk meets Hawk - Both get -2 (fight)

Hawk meets Dove - Hawk gets 2, Dove gets 0 (steal)

Dove meets Dove - both get 1 (share)

My notes then show:

• Θ_D = λ + P_D * 1 + P_H * 0

• Θ_H = λ + P_D * 2 + P_H * -2

P_D is the probability of meeting a dove (the proportion of doves in the population). I'm wondering what exactly theta and lambda mean here. My instinct is that Θ_D would represent the expected pay-off for a dove, but the use of the lambda (which is apparently equal to 3) throws me off here. What is the point in lambda and what does it represent? --80.4.203.142 (talk) 12:22, 25 May 2008 (UTC)

:Hm... not sure. I should check out my EGT bibliography. If memory serves, θ may mean specific total fitness (i.e. offspring each "strategy" will cast), while λ would stand for a base fitness.

:Oh, it is apparently so: Here is a web link that explains this setting: [http://plato.stanford.edu/entries/game-evolutionary/#2]. Pallida  Mors 15:32, 26 May 2008 (UTC)

::Thanks! --80.4.203.142 (talk) 21:40, 26 May 2008 (UTC)

Why don't they standardise the t-distribution so that the variance is always 1? After all, it is already a general, standardised, distribution, because in getting a t-statistic, which comes from a t-distribution (typically if we add the assumption of the null hypothesis in practical applications), you divide by the standard error. Thanks in advance, 203.221.126.247 (talk) 12:59, 25 May 2008 (UTC)

:Apart from anything else, there is the problem that a t₁ hasn't got a variance, and t₂ has variance infinity. Algebraist 16:37, 25 May 2008 (UTC)

:It's because the distribution is interesting because it has a certain number of relationships with other distributions, (in particular, see the bottom of http://en.wikipedia.org/wiki/Student_t_distribution#Derivation) which would be broken if it's 'standardised'.--Fangz (talk) 22:32, 25 May 2008 (UTC)

Thanks, that makes sense. I figured it was something like that, but I asked because I had previously taken for granted the idea that the t-distribution had a variance of 1, by analogy with the normal (they both arise in statistics from dividing by a standard deviation-like quantity). 130.95.106.128 (talk) 11:03, 29 May 2008 (UTC)