Investment Studio > Expressions > Functions > Statistical > NORMDIST
float normdist(float x, float mean, float standard_deviation, boolean cumulative = TRUE)
Returns the normal (also known as Gaussian, or "bell curve") probability function.
x is the point of evaluation.
standard_deviation must be > 0.
If mean = 0 and standard_deviation = 1, normdist reduces to normsdist (standard normal distribution).
If cumulative = TRUE, the CDF (Cumulative Distribution Function) is returned (equal to the probability that x is >= a stochastic variable with normal distribution); otherwise, the PDF (Probability Density Function) is returned. If omitted, cumulative defaults to TRUE.
Mathematically, the normal PDF (with m = mean and s = standard deviation) is
| -(x - m)2 / (2 s2) | |
| e | |
| f(x, m, s) = | ¾¾¾¾¾¾¾ |
| (2ps)1/2 |
It can be derived as the continuous limit of the binomial distribution for large numbers of trials with finite success probability (see binomdist). The normal CDF is
| x | ||
| F(x, m, s) = | ó | f(u, m, s) du |
| ô | ||
| õ | ||
| -¥ |
The normal distribution has a wide range of applications. In particular, the distribution of the arithmetic average of a large number N of measurements of a stochastic variable is normal with standard deviation N-1/2 times that of the variable's distribution, independently of the shape of the variable's own distribution (central limit theorem). This is the theoretical foundation for the central role played by the normal distribution in error estimation and hypothesis testing, and the rationale for assuming stochastic variables with unknown distributions to be normal (often done e.g. in physics).
Example
=normdist(1, 2, 3, TRUE)
returns 0.369441340183258;
=normdist(1, 2, 3, FALSE)
returns 0.125794409230998.
See also norminv, normsdist, normsinv, standardize, ztest.