Property	Value
Hex Value	`$BB11`
Categories	Catalog > I Statistics > Distributions
Localizations	FR: `FracNormale(`

`invNorm(`

Overview

Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by μ and s.. The optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a. The tokens LEFT, CENTER and RIGHT can be found in [catalog].

Availability: Token available everywhere.

Syntax

invNorm(area[,µ,σ,tail])

Arguments

Name	Type	Optional
area
µ
σ
tail

Location

2nd, distr, DISTR, 3:invNorm(

Description

invNorm( is the inverse of the cumulative normal distribution function: given a probability, it will give you a z-score with that tail probability. The probability argument of invNorm( is between 0 and 1; 0 will give -1E99 instead of negative infinity, and 1 will give 1E99 instead of positive infinity

There are two ways to use invNorm(. With three arguments, the inverse of the cumulative normal distribution for a probability with specified mean and standard deviation is calculated. With one argument, the standard normal distribution is assumed (zero mean and unit standard deviation). For example:

for the standard normal distribution
:invNorm(.975

for the normal distribution with mean 10 and std. dev. 2.5
:invNorm(.975,10,2.5

Advanced

This is the only inverse of a probability distribution function available (at least on the TI-83/84/+/SE calculators), so it makes sense to use it as an approximation for other distributions. Since the normal distribution is a good approximation for a binomial distribution with many trials, we can use invNorm( as an approximation for the nonexistent "invBinom(". The following code gives the number of trials out of N that will succeed with probability X if the probability of any trial succeeding is P (rounded to the nearest whole number):

:int(.5+invNorm(X,NP,√(NP(1-P

You can also use invNorm() to approximate the inverse of a t-distribution. Since a normal distribution is a t-distribution with infinite degrees of freedom, this will be an overestimate for probabilities below 1/2, and an underestimate for probabilities above 1/2.

Formulas

Unlike the normalpdf( and normalcdf( commands, the invNorm( command does not have a closed-form formula. It can however be expressed in terms of the inverse error function:

(1) $\begin{align} \texttt{invNorm}(p) = \sqrt{2}\,\texttt{erf}^{-1}(2p-1) \end{align}$

For the arbitrary normal distribution with mean μ and standard deviation σ:

(2) $\begin{align} \texttt{invNorm}(p,\mu,\sigma)=\mu+\sigma\texttt{invNorm}(p) \end{align}$

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, thornahawk.

History

Calculator	OS Version	Description
TI-83	0.01013	Added

Last update: September 30, 2023 15:38:51
Created: February 23, 2023 23:15:01

Authors: Adrien Bertrand

invNorm(