Table of Contents
An inverse normal distribution is a type of probability distribution that is the reverse of a normal distribution. It is also known as a reversed normal distribution and is used to model the probability of rare events. It is commonly used in risk analysis and reliability engineering. It is a symmetrical distribution, so the mean, median, and mode are all the same. The probability of events is highest in the center and decreases as it moves away from the center.
The term inverse normal distribution refers to the method of using a known probability to find the corresponding z-critical value in a .
This is not to be confused with the , which is a continuous probability distribution.
This tutorial provides several examples of how to use the inverse normal distribution in different statistical softwares.
Inverse Normal Distribution on a TI-83 or TI-84 Calculator
You’re most likely to encounter the term “inverse normal distribution” on a TI-83 or TI-84 calculator, which uses the following function to find the z-critical value that corresponds to a certain probability:
invNorm(probability, μ, σ)
where:
- probability: the significance level
- μ: population mean
- σ: population standard deviation
You can access this function on a TI-84 calculator by pressing 2nd and then pressing vars. This will take you to a DISTR screen where you can then use invNorm():
For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:
The z-critical value that corresponds to a probability value of 0.05 is -1.64485.
Related:
Inverse Normal Distribution in Excel
To find the z-critical value associated with a certain probability value in Excel, we can use the INVNORM() function, which uses the following syntax:
INVNORM(p, mean, sd)
- p: the significance level
- mean: population mean
- sd: population standard deviation
For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:
The z-critical value that corresponds to a probability value of 0.05 is -1.64485.
Inverse Normal Distribution in R
To find the z-critical value associated with a certain probability value in R, we can use the function, which uses the following syntax:
qnorm(p, mean, sd)
where:
- p: the significance level
- mean: population mean
- sd: population standard deviation
For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:
qnorm(p=.05, mean=0, sd=1) [1] -1.644854
Once again, the z-critical value that corresponds to a probability value of 0.05 is -1.64485.