# binomial_random_vars_are_different

2021年6月19日

この関数は、2つの2項分布確率変数が同じパラメータを持つかどうかをチェックするための単純な統計的検定を実行します（つまり、 “成功"の可能性）。次の論文で説明されている単純尤度比検定を使用します。

Dunning, Ted. 「 Accurate methods for the statistics of surprise and coincidence. （驚きと偶然の統計の正確な方法）」 Computational linguistics 19.1 (1993): 61-74

そのため、この方法の詳細については上記の論文を参照してください。

#include <dlib/statistics/statistic.h>

```    double binomial_random_vars_are_different (
uint64_t k1,
uint64_t n1,
uint64_t k2,
uint64_t n2
);
/*!
requires
- k1 <= n1
- k2 <= n2
ensures
- Given two binomially distributed random variables, X1 and X2, we want to know
if these variables have the same parameter (i.e. the chance of "success").
So assume that:
- You observed X1 to give k1 successes out of n1 trials.
- You observed X2 to give k2 successes out of n2 trials.
- This function performs a simple likelihood ratio test to determine if X1 and
X2 have the same parameter.  The return value of this function will be:
- Close to 0 if they are probably the same.
- Larger than 0 if X1 probably has a higher "success" rate than X2.
- Smaller than 0 if X2 probably has a higher "success" rate than X1.
Moreover, the larger the absolute magnitude of the return value the more
likely it is that X1 and X2 have different distributions.
- For a discussion of the technique and applications see:
Dunning, Ted. "Accurate methods for the statistics of surprise and
coincidence." Computational linguistics 19.1 (1993): 61-74.
!*/

```