Inverse cumulative normal distribution is a statistical function that calculates the probability of obtaining a certain value or lower from a normal distribution. It is also known as the probit function or the inverse normal function.
Inverse cumulative normal distribution is useful in many statistical applications, such as hypothesis testing, confidence intervals, and regression analysis. It allows us to calculate probabilities and determine critical values for a given normal distribution.
The inverse cumulative normal distribution is typically calculated using a statistical software or a table of values. Most statistical software programs have built-in functions for calculating the inverse normal distribution, such as Excel's NORM.INV function. The table method involves finding the closest value to the desired probability and then interpolating to get the corresponding z-score.
Inverse cumulative normal distribution is closely related to the standard normal distribution, which is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. The inverse normal function takes a probability value as input and returns the corresponding z-score from the standard normal distribution.
Inverse cumulative normal distribution is commonly used in fields such as finance, economics, psychology, and engineering. It is used in hypothesis testing to determine critical values and p-values, in confidence interval calculations, and in calculating probabilities for normal distributions.