Help with a StatisticsEquation/Decay Formula from an Article

[ncampbell]

Hi,

I am more of a language student and not a math student so I am really struggling with some math equations. I am trying to understand an article with a decay formula for ancient Hebrew (my area of study) and plotting word frequencies on a log graph but I can't make sense of what the author is saying. this is his formula:

f_2c(r, t) = A_2cf₀(r)exp[-k(f₀(r))t]
t = 7.8 kyr andA_2c=3.

k(f₀)=B/(3.27f₀)^β
B = 0.55 kyr^-1 and β = 0.13

some of the items I understand like 2c = the type/item (biconsonantal roots), t = time, r= rank, and I believe exp = exponential logarithm (?)
So using the most frequent word in this category (3576 occurrences, rank 1) I try to do it as:
k(3576)=B/(3.27*3576)^β
k(3576) = 1.818181818/(3.27*3576)^β
k(3576) = 1.818181818/(11693.52)^β
k(3576) = 1.818181818/3.379347744
k(3576) = 0.5380274407

If I did this right (which I am not sure if I did) then I think I plug it into the first equation under k?
f2c(1, 7.8) = A2c(3576)(1)exp[-.5380274407(3576(1))7.8]
BUT exp[−15007.0918]= 0???
I have no idea what I am doing wrong here.

However, overall I have tried to input some of his data and get his answers but I can't seem to make that happen. Could someone give me a key to what the letters are asking for or even just 1 example with the numbers filled in so I can see what they are doing? If I could get the equation right 1 time, then I would know what to fill in for each number and can understand the calculation.
This is the full article: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0083780


Any help would be greatly appreciated! I am driving myself nuts trying to figure out what they are doing!

Thank you,
Nick

 

[JeffM]

I have glanced at the cited paper. It is not my field. But the standard meaning of

[MATH]exp(u) = e^u, \text { where } e \approx 2.718 \implies f_{2c} = \dfrac{3 * f_0(r)}{e^{k(f_0(r)) *t}}[/MATH]
I can't say I like the paper's presentation or notation. The math is not all in a single section where it can be read coherently, and the analytics of the regression analysis do not seem to be specified anywhere. f is first introduced as a variable dependent on A and alpha, but later it is said that f is dependent on A and alpha₀ or alpha₁. Even later, we start dealing with f₀, f_2c, and f_3c. I did not see anywhere where the relationship between what now seem to be symbols for functions of r and t is defined.

[MATH]k(f_0) = \dfrac{B}{(3.27f_0)^{\beta}} = \dfrac{0.55}{(3.27f_0)^{0.13}}[/MATH]
is soluble if we know f₀(r). I did not see it specified in the article. That does not mean it's not there. But I don't see how you can do anything without it.

Someone else may be help you decipher the math, but, to my eye, it looks as though the math is presented in a deliberately obscure way to prevent anyone from assessing the paper's math.