| Property | Value |
|---|---|
| Hex Value | $BB11 |
| Categories | |
| Localizations |
|
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(
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
tail [catalog]: LEFT, CENTER, RIGHT
Arguments
| Name | Type | Optional |
|---|---|---|
| tail catalog: LEFT | ||
| CENTER | ||
| RIGHT |
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) \(\begin{align} \texttt{invNorm}(p,\mu,\sigma)=\mu+\sigma\texttt{invNorm}(p) \end{align}\)
Related Commands
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 |