Inverse Normal distribution
This tool calculates the Inverse of Normal Cumulative Distribution Function. One of its uses is to calculate percentiles of a Normal distribution.
Inverse Normal Distribution formulas
X : a random variable with a normal distribution
`mu` : mean of variable X
`sigma` : its Standard deviation
The inverse of the cumulative distribution function is also called the 'quantile function'.
We denote Q the quantile function and F the cumulative distribution function of variable X. We have,
`F(x) = 1/(sigma*sqrt(2pi))*\int_-oo^xe^(-1/2*(t-mu)^2/sigma^2)\ dt`
`Q(x) = F^(-1)(x)`
For a probability p, quantile function Q gives a q value that verifies,
`q = Q(p) = F^(-1)(p)`
By definition of F, we have,
`P(X < q) = p`
`P(X < q)` is the pobability that X is less than q.
In addition to quantiles, this tool calculates, for a given probability p, the values q such that,
`P(X > q) = p`
`P( |X - mu| < q) = p`
`P( |X - mu| > q) = p`
Example of use : quartiles calculatorTo calculate the first quartile Q1 (or 25th percentile) of the standard Normal distribution, we input the following values in the calculator,
`mu = 0`
`sigma = 1`
We get, Q1 = -0.67448975
for p = 0.75, we get Q3 = 0.67448975
for p = 0.5, we get the mean as expected, Q2 = 0.