Dax Function: NORM.S.DIST

Category: Statistical Functions

The NORM.S.DIST function in Power BI is a DAX (Data Analysis Expressions) function used to calculate the standard normal cumulative distribution function (CDF) or the probability density function (PDF). It assumes a mean of 0 and a standard deviation of 1, focusing on the standard normal distribution.

Purpose of the Function

To evaluate the probability or cumulative probability of a given z-score within the standard normal distribution.

Type of Calculations

Computes cumulative probability (area under the curve) or the probability density for a given z-score.

Practical Use Cases

  • Evaluate probabilities in hypothesis testing.
  • Compute z-score percentiles.
  • Analyze deviations from the mean in standardized datasets.

NORM.S.DIST(<z>, <cumulative>)</cumulative></z>
ParameterTypeDescription
<Z>ScalarThe zz-score for which the distribution is evaluated. Represents the number of standard deviations from the mean.
<Cumulative>BooleanDetermines the type of distribution to compute: TRUE for cumulative probability (CDF), FALSE for probability density (PDF).

How Does NORM.S.DIST Dax Works

Mathematical Principle

The function evaluates the standard normal distribution formula:

  1. Probability Density Function (PDF):

  2. Cumulative Distribution Function (CDF):

    Where:

    • z is the input z-score.

    • e is the base of the natural logarithm.

What Does It Return?

The NORM.S.DIST function returns:

  • A numeric value:

    • If <Cumulative> is TRUE, it returns the cumulative probability.

    • If <Cumulative> is FALSE, it returns the probability density at the specified zz-score.

  • Values range between 0 and 1.

When Should We Use It?

  • Standardized Datasets: Analyze data that has been normalized to a standard normal distribution.

  • Statistical Analysis: Calculate probabilities or densities for zz-scores in hypothesis testing or quality control.

  • Percentile Analysis: Find where a data point falls in the standard normal distribution.

Examples

Basic Usage :

Find the cumulative probability for a z-score of 1.5:


NORM.S.DIST(1.5, TRUE)

Output: Approximately 0.9332 (the cumulative probability up to z = 1.5 ).

Column Usage

Apply the function to a column of zz-scores to compute cumulative probabilities:


ADDCOLUMNS(
Scores,
"CumulativeProbability",
NORM.S.DIST(Scores[ZScore], TRUE)
)

Use Case: Add a column showing cumulative probabilities for each -score in the dataset.

Advanced Usage

Combine with filtering to find cumulative probabilities for a subset of data:


CALCULATE(
NORM.S.DIST(Sales[ZScore], TRUE),
Sales[Category] = "Electronics"
)

Use Case: Compute probabilities specific to the “Electronics” category.

Tips and Tricks

  • Boolean Parameter: Use TRUE for cumulative probabilities and FALSE for density values to avoid confusion.

  • Input Validation: Ensure zz-scores are valid and represent standard deviations from the mean.

  • Preprocessing: Standardize datasets before applying the function for meaningful results.

Performance Impact of NORM.S.DIST DAX Function:

  • Efficient for small-to-medium datasets.

  • For large datasets, consider precomputing values if probabilities need frequent recalculations.

Related Functions You Might Need

  • NORM.DIST: Calculates probabilities for normal distributions with custom mean and standard deviation.

  • NORM.INV: Finds the zz-score for a given cumulative probability.

  • PERCENTILEX.INC: Computes percentiles in datasets.

Want to Learn More?
For more information, check out the official Microsoft documentation for NORM.S.DIST You can also experiment with this function in your Power BI reports to explore its capabilities.

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1. What does the NORM.S.DIST function do in Power BI?

It calculates the cumulative probability or density of a given zz-score in the standard normal distribution.

2. What is the difference between cumulative and density in NORM.S.DIST?

Cumulative (TRUE) calculates the probability up to a zz-score, while density (FALSE) computes the height of the distribution curve at z.

3. Can I use non-standard distributions with NORM.S.DIST?

No, it is specifically designed for the standard normal distribution (mean = 0, standard deviation = 1).

4. What is the range of values returned by NORM.S.DIST?

The range is between 0 and 1, representing probabilities.

5. Is the function efficient for large datasets?

Yes, but for frequent calculations, precomputing values may improve performance.

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