As long as p <= 1, the minimum value of H will be log(m). Here are some more (I think clearer) graphs. They show the basic function p[,i] * log(p[,i] (the log function defaults to natural logarithm), for values ranging from 0 to 1. Then include log(m) for different values of m. I included the code, and also attached a PDF in incase there was any trouble running the code.
x <- seq(0, 1, by = .01)
par(mfrow = c(3, 2))
plot(x = x, y = log(x ^ x), type = "l",
ylab = bquote(f(x) == ln(x^x)), main = "Basic graph")
plot(x = x, y = -log(x ^ x), type = "l",
ylab = bquote(f(x) == -ln(x^x)), main = "Basic negative graph")
plot(x = x, y = log(0.5) - log(x ^ x), type = "l",
ylab = bquote(f(x) == ln(0.5) - ln(x^x)), main = "m = 0.5")
plot(x = x, y = log(1) - log(x ^ x), type = "l",
ylab = bquote(f(x) == ln(1) - ln(x^x)), main = "m = 1")
plot(x = x, y = log(2) - log(x ^ x), type = "l",
ylab = bquote(f(x) == ln(2) - ln(x^x)), main = "m = 2")
plot(x = x, y = log(6) - log(x ^ x), type = "l",
ylab = bquote(f(x) == ln(6) - ln(x^x)), main = "m = 6")
So the way I see it, you have 3 ways to get different values:
1) Increase your matrix p
2) Decrease m
3) Increase your selection region (this in turn depends on alpha, the
mean, and the standard deviation)
Cheers,
Josh
On Sun, Sep 26, 2010 at 7:58 PM, jethi <kart...@hotmail.com> wrote:
>
> wow thnx a lot josh. so now i understand the most of the things. so my power
> function is depent on the number of the blocks "m". how u said, if i take
> m=0.8 or lower i get a different value than a 1. ofcourse a number between
> 0 or 1. but i can just take positive interger number for m, because m
> representet die value for the blocks and they could be only a positiv
> number. moreover the graphic show that my H will never reach log(m) because
> like u said p are probilities. so if i would now plot the powerfunction for
> different m(positiv integer), the graph would be a constant value. am i
> right?
>
> thank u very very much. its help me a lot.
> --
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>
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--
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/
graphs.pdf
Description: Adobe PDF document
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