예제: 확률 밀도 및 누적 확률 분포

함수 > 통계 > 확률 분포 > 예제: 확률 밀도 및 누적 확률 분포

dnorm, pnorm, cnorm 및 qnorm 함수를 사용하여 여러 확률 함수 간의 차이를 나타냅니다.

1. 정규 분포의 평균과 표준 편차를 정의합니다.

2. 정규 분포의 확률 밀도(파란색)와 누적 확률(검정색 및 빨간색)을 도표화합니다.

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dnorm 함수는 평균이 μ이고 표준 편차가 σ일 때 x에서 정규 분포의 확률 밀도를 계산합니다. pnorm 함수는 정규 분포의 누적 확률 분포를 계산합니다. cnorm 함수는 μ = 0이고 σ = 1인 정규 분포의 누적 확률 분포입니다.

3. qnorm 함수를 사용하여 곡선 아래의 - ∞ 및 x 사이 구역이 전체 곡선 아래 구역의 절반일 때 x 값을 계산합니다.

이 예제의 경우 다음 수식으로 확인되듯이 x의 값이 평균과 같습니다.

q에서의 확률 밀도는 qnorm 함수의 역인 pnorm 함수로 쉽게 다시 구할 수 있습니다.

4. qnorm 함수를 사용하여 정규 분포의 75번째, 90번째 및 95번째 백분위수를 구합니다.

5. 위에서 계산한 백분위수(75%: 빨간색, 90%: 녹색, 95%: 파란색)를 추가하여 정규 분포의 확률 밀도(파란색)와 누적 확률(검정색)을 도표화합니다.

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