Wikipedia:Reference desk/Archives/Mathematics/2015 March 9

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March 9

Normal distribution uses on political parties.

Hello, I was wondering if it is possible to use the Normal Distribution to show that a political party is unpopular.

For example in UK if a political party got <2.5% of the vote would it move them to the far left of the distribution and render them as eccentrics? — Preceding unsigned comment added by 86.177.220.245 (talk) 09:31, 9 March 2015 (UTC)

Normal distribution allows (with extremely low probability) arbitrary large difference between a sample and the distribution's centre. That appears to contradict a condition of a party popularity measure (based on the 0—100 interval of the votes percentage).

By the way, what if there were 40 parties and each of them gets 2.5%? Are all 'eccentrics'...?

And what would be a 'non-eccentric' party? The one which gets almost exactly 50%? Or that which gets nearly 100%? --CiaPan (talk) 09:59, 9 March 2015 (UTC)

(After EC) The correct question is not whether it's possible, but whether it's proper. The answer is generally no. That a party has little popular support doesn't mean that its supporters correspond to the left tail of a normal curve based on some meaningful measure. If you want to graphically show how little popular support the party has, a pie chart, for example, would be more appropriate. By the way, "eccentric" carries a connotation that's not necessarily implied by being not popular. --173.49.18.106 (talk) 10:22, 9 March 2015 (UTC)

What you could do is model the population of the country by some sort of distribution. You could take a simple left-right distinction or use something like the Political compass which has two axes, see Political spectrum for many different types of model. You then see whee the people who vote for each party lie in this domain and try and fit a distribution to each party. Of course such a system is fraught with difficulty: how can you give a value to political beliefs. One problem is that there is a large geographical component with the north displaying different characteristics to the south.--Salix alba (talk): 07:19, 12 March 2015 (UTC)

Perfect derivative

Defining a perfect derivative as an algebraic function that's the derivative of another algebraic function (similar to defining a perfect square,) is there any general rule you can use in determining whether an algebraic function is a perfect derivative?? Sometimes, 2 functions can be similar, but whether they are perfect derivatives does not match. $1/x^{2}$ is a perfect derivative; it's the derivative of $-1/x$ . But $1/(x^{2}+1)$ is not a perfect derivative. It is the derivative of the inverse tangent, which is not algebraic. Georgia guy (talk) 18:40, 9 March 2015 (UTC)

The information at Risch algorithm might be relevant (though the algorithm itself is for elementary, rather than algebraic, antiderivatives). -- Meni Rosenfeld (talk) 20:27, 9 March 2015 (UTC)