Zoho Sheet LOGINV: Lognormal Percentiles and Inverse CDF

• Introduced: The original introduction version and date are not established by the checked sources.
• Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
• Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
• Checked: October 14, 2026, against the official LOGINV reference. Documentation check; not a new native test.

LOGINV(p; μ; σ)

Zoho prints all three arguments without square brackets; no parameter is documented as optional and there is no documented fourth mode setting. Its English help page uses semicolon separators. Decimal and number formatting depend on workbook locale settings; that documentation does not independently establish a change in function-name availability or parser separators for every locale. [Z-LNI, Z-LOCALE]

An inverse CDF asks the opposite question from LOGNORMDIST. With LOGNORMDIST, you supply x and receive a probability. With LOGINV, you supply a probability and obtain x. The result is expressed in the original positive units—days, dollars or hours—provided μ and σ were fitted on the natural-log scale of those units. [Z-LND, M1]

Enter A, B and C as shown, put =LOGINV(A2;B2;C2) in D2 and fill down. Column E contains model values computed independently with SciPy, not values observed in Zoho Sheet. Use enough numeric display precision to see meaningful comparisons. [M1]

The official Zoho help includes an embedded-sheet example in which =LOGINV(A2;B2;C2) returns 25.947598893. Using the separately documented illustrative inputs p=0.3, μ=4.2, σ=1.8 reproduces that approximate number mathematically. The embedded sheet was not opened or used as native execution evidence. [Z-LNI, M1]

For a no-calculator sanity check, =LOGINV(0.5;0;1) mathematically equals 1 because the median of a lognormal distribution is EXP(μ) and the normal 50th percentile has z-score 0. It does not follow that the mean of the same raw distribution is 1; the raw mean is larger when σ>0. [M1]

Let Y=LN(X) and suppose Y follows a normal distribution with mean μ and standard deviation σ. For 0<p<1, the underlying mathematical percentile is

x(p) = EXP( μ + σ × Φ⁻¹(p) )

where Φ⁻¹(p) is the standard normal quantile. Zoho separately documents NORMSINV(p), so a conceptual comparison using the same units is:

=EXP(B4+C4*NORMSINV(A4))

If B4=0, C4=1 and A4=0.9, the independent expected x is again about 3.602224479279. This is a mathematical equivalence using documented Zoho function names; the source does not state precision or parity guarantees across every Zoho platform or release. [Z-NORMSINV, Z-LNI, M1]

The raw median is EXP(μ) and the raw mean is EXP(μ+σ²/2). Thus, when μ=2, σ=0.5, the expected raw median is approximately 7.389056098931, while the expected raw mean is approximately 8.372897488127. Confusing the raw mean with μ can shift quantiles substantially. [M1]

Assume a hypothetical service organization has verified that positive completion times are approximately lognormal, with median 8 days and log-scale standard deviation 0.6. The organization wants a target that covers 90% of modeled completions. Let D2=8 (median), D3=0.6 (log SD), and D4=0.9 (target coverage). Use:

D5: =LN(D2)
D6: =LOGINV(D4;D5;D3)
D7: =LOGNORMDIST(D6;D5;D3)

The independently calculated cutoff in D6 is 17.259668530947 days, and the mathematical round-trip in D7 is 0.900000000000. Because operational cutoffs are usually whole days, a policy might round up to 18 days using an appropriately checked rounding procedure; this is an external policy choice, not part of LOGINV itself. Do not convert the mathematical percentile into a guaranteed customer promise without evaluating data quality, censoring, calendar effects and how the service-level denominator is defined. [Z-LNI, Z-LND, M1]

For a second risk level, switch D4 to 0.95: the independently computed 95th percentile is 21.463497849743 days. For p=0.99, it is 32.305912599878 days. A 90th-to-99th percentile change can produce a very large absolute increase in a heavily right-skewed model; don’t extrapolate from the median alone. [M1]

Reverse check: For interior p and positive σ, a theoretically consistent forward/inverse pair satisfies:

=LOGNORMDIST(LOGINV(0.95;2;0.5);2;0.5)

The mathematical expected result is 0.95, subject to floating-point precision and the spreadsheet’s numerical implementation. The reverse direction, LOGINV(LOGNORMDIST(x;μ;σ);μ;σ), should mathematically recover valid positive x within numerical precision. These are excellent native-test candidates, but this research performed only independent arithmetic. [Z-LND, Z-LNI, M1]

Estimating parameters: Do not pass raw arithmetic mean and raw standard deviation directly unless you have established that they are the logarithmic parameters. For observed positive measurements, build a helper column of LN(value) and assess whether the transformed distribution is acceptably normal. Missing, zero and censored observations require specific domain treatment. A regression forecast’s residual distribution can differ from the overall distribution of measurements; check model structure before applying one global percentile. [M1]

Threshold versus future observation interval: A population/model percentile is not automatically a confidence interval for an estimated percentile, nor an interval around the mean. Sampling uncertainty in the fitted μ and σ is not accounted for by the simple LOGINV formula. For high-stakes operations, estimate uncertainty separately and validate the model against held-out observations. [M1]

Outlier treatment: A few extreme positive observations strongly affect the fitted log-scale σ and upper-tail percentiles. Retain an audit trail of data cleaning and compare predicted percentiles with empirical quantiles. If the observed data include a point mass at zero, a standalone lognormal distribution cannot represent the entire outcome process. [M1]

The function is documented in Zoho’s general Sheet Help. The individual article does not specify a first-supported version, a separate desktop/mobile evaluation guarantee, an enterprise-account requirement, or a definitive endpoint/overflow policy. These remain unverified rather than being inferred from Excel. [Z-LNI]

Zoho documents LOGINV(p; μ; σ). Microsoft documents legacy Excel LOGINV(probability,mean,standard_dev) and modern LOGNORM.INV(probability,mean,standard_dev); both describe an inverse lognormal CDF. The modern Excel spelling must not be silently treated as a separate Zoho function or confirmed Zoho alias. An Excel file using the dotted name requires explicit Zoho compatibility verification. Microsoft may document boundary and iteration details that Zoho does not; do not transfer those behaviours to Zoho without testing. [Z-LNI, MS-LNI, MS-OLD]

• [Z-LNI] Zoho Sheet, “LOGINV,” purpose, syntax, published example, generic errors, checked 2026-10-13: https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/loginv
• [Z-LND] Zoho Sheet, “LOGNORMDIST,” counterpart CDF, checked 2026-10-13: https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/lognormdist
• [Z-NORMSINV] Zoho Sheet, “NORMSINV,” standard normal quantile, checked 2026-10-13: https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/normsinv
• [Z-LOCALE] Zoho Sheet, “Locale and calculation settings,” checked 2026-10-13: https://help.zoho.com/portal/en/kb/sheet/getting-started-with-zoho-sheet/articles/locale-and-calculation-settings-in-your-spreadsheet
• [MS-LNI] Microsoft, “LOGNORM.INV function,” checked 2026-10-13: https://support.microsoft.com/en-au/office/lognorm-inv-function-fe79751a-f1f2-4af8-a0a1-e151b2d4f600
• [MS-OLD] Microsoft, “LOGINV function,” checked 2026-10-13: https://support.microsoft.com/en-us/excel/loginv-function
• [M1] Independent lognormal percent-point function calculations and algebra using Python/SciPy, dated 2026-10-13. Native Zoho Sheet executions: 0; embedded iframe executions: 0; screenshots: 0.

Native validation: Check parsing, numerical outputs, boundary responses and locale behavior in your own Zoho account before operational use.