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EXPONDIST Function in Apple Numbers: CDF and Density

Statistical Intermediate Apple Numbers

Use Apple Numbers EXPONDIST for exponential cumulative probabilities and density; verified examples, parameter constraints and modelling tips.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Apple Numbers. How formula examples are checked

Quick answer: =EXPONDIST(4,2,1) returns about 0.999664537372097, the exponential cumulative probability for x=4 and rate λ=2; changing the last argument to 0 returns approximately 0.000670925255805024, the distribution’s density at 4. These are two different quantities. Apple documents both results in EXPONDIST help 15.4. [A1, C1]

Exact Apple EXPONDIST syntax, types and defaults

=EXPONDIST(x-value, lambda, function-type)
Position Argument Type Required Accepted values / default
1 x-value Number value Yes x ≥ 0; no default.
2 lambda Number value Yes λ > 0; no default.
3 function-type Modal value Yes TRUE or 1 for CDF; FALSE or 0 for density (PDF). No documented omitted default.

The order is x, lambda, then mode. In particular, lambda is a rate parameter rather than a mean; for an exponential waiting-time model, the mean waiting time is 1/lambda in matching units. The third argument is mandatory in the documented signature and selects either of two outputs. Apple’s modal type definition explains that such a parameter chooses calculation type. [A1, A2, C1]

For reference, the continuous exponential distribution has (for x ≥ 0, λ > 0):

  • Cumulative distribution: P(X ≤ x) = 1 − EXP(−λx); in Numbers use EXPONDIST(x,lambda,TRUE) or EXPONDIST(x,lambda,1).
  • Probability density: f(x) = λ × EXP(−λx); in Numbers use EXPONDIST(x,lambda,FALSE) or EXPONDIST(x,lambda,0).

The density is a height per unit of x, not the probability of an exact point: for a continuous variable, P(X=x)=0. A density can exceed 1 without violating the rules for probabilities (for example, lambda=2 at x=0 gives height 2). The CDF always stays between zero and one mathematically, for allowed inputs. [A1, C1]

Reproducible worksheet: waiting times with a rate of 2

Create a Numbers table called WaitingTimes. Enter Time x in B1, Rate lambda in C1, P(X≤x) in D1 and Density f(x) in E1. Populate B2:B6 and C2:C6 with the numeric values below; in D2 enter =EXPONDIST(B2,C2,1) and in E2 enter =EXPONDIST(B2,C2,0), then fill both formulas down. No array range or dynamic-spill assumption is required. [A1, A3]

Row B: x C: lambda D: CDF formula Expected D E: Density formula Expected E
2 0 2 =EXPONDIST(B2,C2,1) 0 =EXPONDIST(B2,C2,0) 2
3 0.5 2 =EXPONDIST(B3,C3,1) 0.632120558829 =EXPONDIST(B3,C3,0) 0.735758882343
4 1 2 =EXPONDIST(B4,C4,1) 0.864664716763 =EXPONDIST(B4,C4,0) 0.270670566473
5 2 2 =EXPONDIST(B5,C5,1) 0.981684361111 =EXPONDIST(B5,C5,0) 0.0366312777775
6 4 2 =EXPONDIST(B6,C6,1) 0.999664537372 =EXPONDIST(B6,C6,0) 0.000670925255805

At x=0, the cumulative probability is 0, while the density is 2. At x=1, the CDF is about 0.864665: approximately 86.5% of modelled waiting times fall at or below 1 unit. At x=4, the CDF approaches 1 while the density approaches zero. This interpretation presumes the selected exponential waiting-time model, not a claim about observed field data. [C1]

To reference a different Numbers table, Apple’s syntax permits, for example:

=EXPONDIST(WaitingTimes::B4,WaitingTimes::C4,1)

It is expected to return 0.864664716763 because row 4 contains x=1, lambda=2. If the table is on another sheet, select its cells in the Formula Editor and let Numbers create the sheet-qualified reference; Apple documents sheet and table identifiers separated by ::. [A3, C1]

Apple’s two published examples

Apple explicitly gives =EXPONDIST(4,2,1) → 0.999664537372097 (CDF) and =EXPONDIST(4,2,0) → 0.000670925255805024 (density). Both match independent evaluations of 1−e^(−8) and 2e^(−8), respectively, within ordinary floating-point rounding. [A1, C1]

Using TRUE instead of 1 and FALSE instead of 0 is documented for the third argument. It does not make density equal to probability at the point. Apple does not document the result of omitting the third argument; do not assume a default or copy a different spreadsheet application’s optional-mode convention. [A1]

Advanced applications: intervals, survival and rate modelling

Probability that waiting time lies between two thresholds

If λ=2, the probability of waiting longer than 1 but at most 2 units is a difference of cumulative probabilities:

=EXPONDIST(2,2,1)-EXPONDIST(1,2,1)

Expected value: 0.117019644348 (roughly 11.70%). The model calculates P(1<X≤2); this is not the sum of density heights at 1 and 2. [C1]

Tail probability (survival function)

For a model with lambda=0.5 per hour, the probability of waiting longer than three hours is:

=1-EXPONDIST(3,0.5,1)

Expected result: 0.223130160148, around 22.31%. This is EXP(-lambda*x) under the mathematical exponential model. Distinguish this tail probability from the CDF (probability of waiting at most three hours). [C1]

Rate versus mean, and unit consistency

If mean waiting time is estimated as 5 minutes under this model, the matching rate is lambda=1/5=0.2 per minute. To find P(X≤10 minutes):

=EXPONDIST(10,1/5,1)

Expected result: 0.864664716763. Do not use lambda 5 when the mean is five minutes; that would represent a rate of five events per minute and a 0.2-minute mean. Also avoid mixing a per-hour lambda with x entered in minutes. [C1]

Errors, domain boundaries and troubleshooting

Symptom or example Cause / documented rule Safe response
=EXPONDIST(-1,2,1) Apple requires x ≥ 0. Correct the underlying time or measurement scale; negative elapsed waiting time is invalid in the model.
=EXPONDIST(1,0,1) Apple requires lambda > 0. Enter a positive model rate. Zero is outside the parameter domain.
=EXPONDIST(1,2) The help signature requires three parameters. Supply explicit TRUE/1 for CDF or FALSE/0 for density.
=EXPONDIST(1,2,2) Apple documents only TRUE/FALSE or 1/0 as modal choices. Use a documented third-argument value; other coercion behaviour was not tested.
Density > 1, e.g. 2 at x=0, lambda=2 A density height is not a probability. Set final argument to 1 for a cumulative probability.
Unexpected result on imported sheet Argument separator, translated name, decimal separator, source cell type or units may differ. Check locale and inspect numeric cells before comparing results.
A blank/text cell or an extreme numeric argument Apple’s function entry does not enumerate all coercion/error strings or precision limits. Run a native test in the actual Numbers release; this guide does not invent an error code.

For general formula diagnosis, see Apple’s error guidance. [A1, A4]

Apple’s English examples use EXPONDIST(4,2,1) with commas. Apple’s Brazilian Portuguese 15.4 function page instead labels it DISTEXPON and documents =DISTEXPON(4; 2; 1) using semicolons and a decimal comma in its output. This is a directly verified localised alias for this documentation page. Never assume an English-language formula string can be pasted unchanged into every language edition. [A9]

Apple places LOGNORMDIST in the related-function link on the EXPONDIST reference page; the LOGNORMDIST official URL was checked. Its mathematical distribution is different, so do not substitute it without a model choice. The exponential expressions above explain the independent mathematics; the expected results were checked against Apple’s EXPONDIST help, not against any undocumented implementation detail of the Numbers calculation engine. [A1, C1]

Mac/iPhone compatibility is documented only as the current Numbers 15.4 help/release context, not as an app execution test. No Microsoft Excel or Google Sheets behaviour, including whether modes are optional, was imported into this tutorial. Other spreadsheet products may have comparable exponential distribution functions but require their own verification.

Platform, version, locale and validation boundaries

This guide uses the English Apple Formulas and Functions Help 15.4; the reference explains formula arguments for Numbers and the wider iWork functions browser, not a live test in any particular installation. Apple’s Numbers 15.4 Mac and iPhone user guides describe the current release and OS requirements (Mac: macOS 26 or later; iPhone: iOS 26 or later). Apple’s release notes say new statistical functions were added in 15.4, but they do not individually certify this formula on older releases. Check Numbers > About Numbers on Mac or the iPhone app version and test on your own device if backwards compatibility matters. [A5, A6, A7, A8]

The formulas here use the English-language identifiers and decimal points; English examples separate multiple arguments with commas. Formula names, numeric punctuation and argument separators are locale-dependent. For example, Apple’s Brazilian Portuguese help translates EXPONDIST as DISTEXPON and shows semicolons as separators with decimal commas; do not create a second English-language function page or silently replace a translated name with an English name in that environment. This regional demonstration establishes a specific documented locale example, not a blanket rule for every locale. [A9]

All displayed results are mathematically derived expected values, with checks in an independent Python calculation harness. The documentation and links were inspected on 2026-10-13 (UTC). No Apple Numbers workbook was executed and no screenshot, production link, Excel import/export behaviour, coercion for every cell type, or installed-version compatibility was tested. Differences in rounding or presentation can occur if the cell’s displayed number format has fewer decimals. [C1]

Apple references and verification methods