Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
data_analysis:probability_distributions [2023/02/25 16:45] prgram |
data_analysis:probability_distributions [2023/02/25 18:23] (current) prgram [Probability Distributions] |
||
---|---|---|---|
Line 1: | Line 1: | ||
====== Probability Distributions ====== | ====== Probability Distributions ====== | ||
+ | {{INLINETOC}} | ||
===== Discrete ===== | ===== Discrete ===== | ||
Line 26: | Line 26: | ||
실패 r번, 성공 k번 | 실패 r번, 성공 k번 | ||
+ | ** 실패횟수에 초점 ** | ||
$X \sim \text{NegBin}(k, p)$ or $X \sim \text{NegBin}(r, p)$, depending on the parameterization used. The two parameterizations are related by the identity $r = k - 1$. | $X \sim \text{NegBin}(k, p)$ or $X \sim \text{NegBin}(r, p)$, depending on the parameterization used. The two parameterizations are related by the identity $r = k - 1$. | ||
Line 33: | Line 34: | ||
=== how? === | === how? === | ||
+ | ** 성공횟수에 초점** | ||
m번실험 시도에 n번 성공 -> m-1번째까지 n-1번 성공 & m번째 성공 | m번실험 시도에 n번 성공 -> m-1번째까지 n-1번 성공 & m번째 성공 | ||
- | $$P(N=n) = {m-1 \choose n-1} p^{n-1} (1-p)^{m-n} p $$ | + | $$P(Y=n) = {m-1 \choose n-1} p^{n-1} (1-p)^{m-n} p $$ |
$n=k$ (성공횟수) -> $m=r+k$ -> $ m-n = r $ | $n=k$ (성공횟수) -> $m=r+k$ -> $ m-n = r $ | ||
$ {k+r-1 \choose r} = {k+r-1 \choose k-1} $ | $ {k+r-1 \choose r} = {k+r-1 \choose k-1} $ | ||
Line 46: | Line 48: | ||
$$P(X = x) = p(1-p)^{x-1}$$ | $$P(X = x) = p(1-p)^{x-1}$$ | ||
+ | |||
+ | ==== Poisson ==== | ||
===== Continuous ===== | ===== Continuous ===== |