Beta distribution / NetLogo feature

Question

I use the statistics extension in NetLogo to calculate the beta function:

set z (stats:beta (H + 1) (T + 1))

Where H and T - the number of goals and tails in the transfer of coins. Using the statistics extension is not significant, I have the same problem when using the factorial beta function expression.

The problem is that when H + T > 168, NetLogo reports z = 0and there are some procedures that I cannot perform [in particular, the beta distribution]

Is there a way to approximate the beta function (or distribution) in Netlogo so that it does not encounter this problem?

Many thanks!

Answer 1

- . , . , - . , 171! , . , .

- :

B (, ) = (-1)! (-1)!/( + - 1)!

, , , ; . , , , , , .

, , :

to-report betafunc [alpha beta]
  ifelse (alpha >= beta)
  [let v1 (factorial (beta - 1) (0))
   let v2 (factorial (alpha + beta - 1) (alpha - 1))
   report (v1 / v2)]
  [let v1 (factorial (alpha - 1) (0))
   let v2 (factorial (alpha + beta - 1) (beta - 1))
  report (v1 / v2)]
end

to-report factorial [n m]
 if (n = m) [report 1]
 report (n * factorial (n - 1) (m))
end

, . , .

, (5! 8!)/(12)! (1,6). (1,7/11). (1,7/11). (3,6/10)... (1.4/8). (1.3/7)... (1.1/5) (1.1/4)... (1.1/1)

, , . :

to-report stepwisefactorial3 [n1 n2 d]
  if (n1 = 0) [report stepwisefactorial2 (n2) (d)]
  if (n2 = 0) [report stepwisefactorial2 (n1) (d)]
  if (d = 0)  [report (stepwisefactorial1 (n1) * stepwisefactorial1 (n2))]
  report ((((n1 * n2) / d)) * stepwisefactorial3 (n1 - 1) (n2 - 1) (d - 1))
end

to-report stepwisefactorial2 [n d]
  if (n = 0) [report (1 / (stepwisefactorial1 (d)))]
  if (d = 0) [report stepwisefactorial1 (n)]
  report ((n / d)* stepwisefactorial2 (n - 1) (d - 1))
end

to-report stepwisefactorial1 [d]
  if d = 0 [ report 1 ]
  report d * stepwisefactorial1 (d - 1)
end

, + a > 345; .

, !

Answer 2

, Gamma, : loggamma. 171, , , a b 172.

observer> show stats:beta 85 86
observer: 1.2864854397253604E-52
observer> show exp (stats:loggamma 85 + stats:loggamma 86 - stats:loggamma (85 + 86))
observer: 1.2864854397251408E-52
observer> show stats:beta 86 86
observer: 0
observer> show exp (stats:loggamma 86 + stats:loggamma 86 - stats:loggamma (86 + 86))
observer: 6.394810665301235E-53
observer> show exp (stats:loggamma 200 + stats:loggamma 200 - stats:loggamma (200 + 200))
observer: 9.713217247613997E-122

(v1.4.0) "bigBeta", .

Answer 3

( , .)

.

Beta(x,y) = Gamma(x) * Gamma(y) / Gamma(x + y)
= exp ( ln(Gamma(x)) + ln(Gamma(y)) - ln(Gamma(x + y)) )

- , Stats , , , , .

observer> show stats:gamma 171
observer: 7.257415615308E306
observer> show stats:gamma 172
observer: Infinity

( http://www.stata.com/support/faqs/statistics/calculating-beta-function/.)