NORMDIST函数没有给出正确的输出 [英] NORMDIST function is not giving the correct output

问题描述

我试图在Excel中使用 NORMDIST 函数创建一个响铃曲线，但输出是奇怪的。

我的意味着是 0,0000583 和标准差是 0,0100323 所以当我将其插入函数 NORMDIST（0,0000583; 0,0000583; 0,0100323; FALSE） code>我希望得到一些接近 0,5 的东西，因为我使用相同的值，因为该值的平均概率应为 50％，但该函数给出了 39,77 的输出，这显然不正确。

为什么会这样？

解决方案

值大于1，但密度可以。

密度函数的整个范围的积分等于1，但它可以具有大于特定间隔的值。 ，说明如何使用NORMIDIST在给定的间隔获得概率，以及在何种情况下可以返回大于1的密度。 / p>

对于连续变量，任何特定值的概率为零，因为有无数个值。

如果您想知道正态分布的连续随机变量在a到b的范围内的概率，请使用：

= NORMDIST（b，mean，dev，TRUE） - NORMDIST（a，mean，dev，TRUE）

密度函数的峰值出现在平均值即= NORMDIST（mean，mean，dev，FALSE）），值为：

= 1 /（SQRT（2 * PI（））* dev）

峰值当您的偏差小于1 / sqrt（2pi）〜0.399，

时，e将超过1。 >

这是一个惊人的答案非常周密地解决了这个问题。

I'm trying to use NORMDIST function in Excel to create a bell curve, but the output is strange.

My mean is 0,0000583 and standard deviation is 0,0100323 so when I plug this to the function NORMDIST(0,0000583; 0,0000583; 0,0100323; FALSE) I expect to get something close to 0,5 as I'm using the same value as the mean probability of this value should be 50%, but the function gives an output of 39,77 which is clearly not correct.

Why is it like this?

解决方案

A probability cannot have values greater than 1, but a density can.

The integral of the entire range of a density function is equal 1, but it can have values greater than one in specific interval. Example, a uniform distribution on the interval [0, ½] has probability density f(x) = 2 for 0 ≤ x ≤ ½ and f(x) = 0 elsewhere. See below:

          

=NORMDIST(x, mean, dev, FALSE) returns the density function. Densities are probabilities per unit. It is almost the probability of a point, but with a very tiny range interval (the derivative in the point).

shg's answer here, explain how to get a probability on a given interval with NORMIDIST and also in what occasions it can return a density greater than 1.

For a continuous variable, the probability of any particular value is zero, because there are an infinite number of values.

If you want to know the probability that a continuous random variable with a normal distribution falls in the range of a to b, use:

=NORMDIST(b, mean, dev, TRUE) - NORMDIST(a, mean, dev, TRUE)

The peak value of the density function occurs at the mean (i.e., =NORMDIST(mean, mean, dev, FALSE) ), and the value is:

=1/(SQRT(2*PI())*dev)

The peak value will exceed 1 when the deviation is less than 1 / sqrt(2pi) ~ 0.399,

which was your case.

This is an amazing answer on Cross Validated Stack Exchange (statistics) from a moderator (@whuber), that addresses this issue very thoughtfully.

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