LOGINV Function: Calculate Lognormal Distribution Inverse Values
=LOGINV(probability, mean, standard_dev)The LOGINV function is a statistical tool designed to calculate the inverse of the lognormal cumulative distribution function. This advanced Excel function is essential for financial analysts, risk managers, and statisticians who need to work with lognormally distributed data, which frequently appears in real-world scenarios such as stock prices, income distributions, and particle sizes. Understanding LOGINV allows you to determine the value at which a specific probability occurs within a lognormal distribution. In practical applications, the LOGINV function helps professionals answer critical business questions: "What stock price corresponds to a 95% probability level?" or "What income threshold represents the 75th percentile in our market analysis?" The function operates by taking a probability value and converting it into the corresponding x-value from a lognormal distribution defined by its mean and standard deviation parameters. This reverse-lookup capability makes LOGINV invaluable for scenario planning, risk assessment, and quantitative analysis across finance, insurance, and research sectors.
Syntax & Parameters
The LOGINV function syntax is structured as =LOGINV(probability, mean, standard_dev), where each parameter plays a distinct role in calculating the inverse lognormal distribution value. The probability parameter must be a value between 0 and 1 (exclusive), representing the cumulative probability level you're investigating—for example, 0.95 for the 95th percentile. The mean parameter refers to the arithmetic mean of the natural logarithm of your dataset, not the mean of the raw data itself; this distinction is crucial for accurate calculations. The standard_dev parameter represents the standard deviation of ln(x), again calculated on the logarithmic transformation of your values, not the original data. Practical implementation requires careful attention to parameter precision. When working with financial data, ensure your mean and standard_dev are calculated using LN() transformations of your actual values. For example, if analyzing stock prices, first apply LN() to each price, then calculate the mean and standard deviation of these logarithmic values. The function returns a single numeric value representing the x-value where the cumulative probability equals your specified probability. Common use cases include determining Value-at-Risk thresholds, setting confidence intervals for forecasts, and establishing percentile-based targets in business planning. Always validate that your probability input falls within the valid range, as values of 0 or 1 will generate errors.
probabilitymeanstandard_devPractical Examples
Financial Risk Management: Stock Price Percentile Analysis
=LOGINV(0.90, 4.5, 0.3)This formula calculates the stock price value at which 90% of the distribution falls below. The mean of 4.5 and standard deviation of 0.3 are pre-calculated from the natural logarithms of historical prices. The result helps establish risk thresholds for portfolio management and Value-at-Risk calculations.
Insurance Claims Analysis: Claim Amount Distribution
=LOGINV(0.75, 8.2, 0.45)This application determines the claim amount below which 75% of all claims fall. Insurance companies use this to establish adequate reserves and pricing strategies. The lognormal distribution is ideal for claim modeling because claim amounts cannot be negative and are right-skewed.
Environmental Science: Particle Size Distribution
=LOGINV(0.50, 2.1, 0.6)At probability 0.50, LOGINV returns the median value of the lognormal distribution. This is particularly useful in environmental monitoring where particle sizes naturally follow lognormal patterns. The median helps characterize typical particle behavior in the distribution.
Key Takeaways
- LOGINV calculates the inverse of the lognormal cumulative distribution function, returning the x-value for a given probability in a lognormal distribution.
- Parameters must be calculated from natural logarithm transformations: mean = AVERAGE(LN(data)) and standard_dev = STDEV(LN(data)), not from raw data.
- Probability must be strictly between 0 and 1 (exclusive); values of exactly 0 or 1 generate #NUM! errors. Use 0.001 or 0.999 for extreme percentiles.
- LOGNORM.INV is the modern replacement for LOGINV in Excel 2010+; use it for new workbooks while LOGINV remains available for legacy compatibility.
- LOGINV is essential for financial risk analysis, insurance modeling, and scientific research where lognormal distributions naturally represent real-world phenomena like stock prices and claim amounts.
Pro Tips
Create a reference table with pre-calculated mean and standard deviation values from your LN() transformations. Store these in named ranges like 'LogMean' and 'LogStdDev' to make LOGINV formulas more readable and maintainable across complex workbooks.
Impact : Dramatically improves formula clarity and reduces errors from recalculating logarithmic parameters. Named ranges make formulas self-documenting and easier to audit.
Validate LOGINV results by cross-checking with LOGNORMDIST. If LOGINV(p, m, s) returns value X, then LOGNORMDIST(X, m, s) should return probability p (within rounding tolerance). This verification catches calculation errors early.
Impact : Ensures accuracy of critical financial and statistical calculations. Prevents propagation of errors into downstream analysis and business decisions.
When working with multiple probability levels (e.g., 25th, 50th, 75th, 90th percentiles), use a helper column with LOGINV formulas rather than manual calculations. This approach scales efficiently and maintains consistency across analyses.
Impact : Increases efficiency when performing multi-level percentile analysis. Reduces manual work and improves consistency in reporting.
Document your mean and standard_dev sources clearly, including the data period and any transformations applied. This metadata is crucial for auditing and when colleagues need to understand or update your analysis.
Impact : Enhances transparency and enables others to validate, reproduce, and improve your statistical models. Critical for compliance and knowledge transfer in organizations.
Useful Combinations
Dynamic Percentile Analysis with IF Logic
=IF(A1>0.5, LOGINV(A1, B1, C1), "Probability too low")Combines LOGINV with conditional logic to validate input and provide meaningful error messages. Useful when building interactive dashboards where users input probability values. The formula only calculates LOGINV if probability exceeds 0.5, otherwise displays a warning message.
Multi-Scenario Analysis with Data Tables
=LOGINV($B$1, OFFSET($B$2, ROW()-2, 0), OFFSET($B$3, ROW()-2, 0))Combines LOGINV with OFFSET for scenario analysis across multiple mean and standard deviation pairs. Enables creating sensitivity tables that show how different distribution parameters affect the resulting percentile values. Particularly useful for stress-testing financial models.
Confidence Interval Calculation
=LOGINV(0.975, B1, C1) - LOGINV(0.025, B1, C1)Uses LOGINV twice to calculate the width of a 95% confidence interval by finding the 97.5th and 2.5th percentile values, then subtracting. This demonstrates how LOGINV enables robust statistical analysis for establishing confidence bounds in business forecasting and risk management.
Common Errors
Cause: The probability parameter is outside the valid range (0 to 1, exclusive). For example, using =LOGINV(1.5, 4.5, 0.3) or =LOGINV(-0.1, 4.5, 0.3) will trigger this error. Also occurs when standard_dev is negative or zero.
Solution: Verify that probability is strictly between 0 and 1 (e.g., 0.95 not 1.95). Ensure standard_dev is positive. Use data validation or conditional checks: =IF(AND(prob>0, prob<1, stdev>0), LOGINV(prob, mean, stdev), "Invalid input")
Cause: One or more parameters contain non-numeric values or text strings. For instance, =LOGINV("0.90", 4.5, 0.3) or referencing cells containing text instead of numbers will produce this error.
Solution: Ensure all parameters are numeric values. Check referenced cells for text formatting. Use VALUE() function to convert text to numbers if necessary: =LOGINV(VALUE(A1), B1, C1). Verify cells don't contain spaces or special characters.
Cause: Formula references deleted cells or invalid cell ranges. This occurs when you reference a cell that has been deleted or when the worksheet structure changes, breaking the formula's references.
Solution: Verify all cell references are valid and the referenced cells still exist. Use the Name Manager to check named ranges. Consider using absolute references ($A$1) for important parameters to prevent accidental changes during copy operations.
Troubleshooting Checklist
- 1.Verify probability parameter is strictly between 0 and 1 (not including 0 or 1). Check for decimal formatting issues that might display 0.90 as 90.
- 2.Confirm mean and standard_dev are calculated from LN() transformations of your raw data, not from the raw data itself. Recalculate using =AVERAGE(LN(range)) and =STDEV(LN(range)).
- 3.Check that all parameters reference valid numeric cells with no text, spaces, or formatting issues. Use VALUE() function if converting text to numbers.
- 4.Validate that standard_dev is positive and non-zero. Negative or zero standard deviation values trigger #NUM! errors.
- 5.Test formula with known values to verify calculations. Cross-check LOGINV results using LOGNORMDIST to ensure accuracy within rounding tolerance.
- 6.Review cell references for absolute vs. relative positioning, especially when copying formulas across worksheets or using in data tables.
Edge Cases
Probability value of 0.5 (median calculation)
Behavior: LOGINV correctly returns the median (50th percentile) of the lognormal distribution. This is a valid use case and produces meaningful results.
The median is particularly useful in lognormal analysis as it better represents the central tendency than the mean for skewed distributions.
Very small standard_dev approaching zero
Behavior: As standard_dev approaches zero, the lognormal distribution becomes increasingly concentrated around the mean. LOGINV will return values very close to EXP(mean) for all probability levels.
Solution: This is mathematically correct behavior. If you observe this pattern, verify that your standard deviation calculation is accurate and not artificially compressed.
This edge case highlights the relationship between distribution spread and LOGINV output variability.
Extreme probability values like 0.00001 or 0.99999
Behavior: LOGINV handles extreme probabilities correctly, returning very low or very high x-values respectively. Results may appear as very large or very small numbers depending on the distribution parameters.
Solution: These calculations are mathematically valid. Use appropriate number formatting to display results meaningfully. Consider using scientific notation for extreme values.
Extreme percentiles are useful for tail-risk analysis in finance, but results become increasingly sensitive to parameter accuracy.
Limitations
- •LOGINV is a legacy function available only in Excel 2007-2010. It has been replaced by LOGNORM.INV in newer versions, and Microsoft may discontinue support in future Excel releases. New workbooks should use LOGNORM.INV instead.
- •The function cannot handle probability values of exactly 0 or 1, limiting its use for theoretical extreme values. Practical applications must use values very close to these limits (0.001, 0.999) rather than the true extremes.
- •LOGINV requires pre-calculated mean and standard deviation of ln(x) values, not the raw data. Users must independently perform logarithmic transformations and statistical calculations, which introduces potential for errors if the transformation process is misunderstood.
- •The function assumes the underlying data follows a true lognormal distribution. If actual data deviates significantly from lognormality, LOGINV results may not accurately represent real-world percentiles. Goodness-of-fit testing should validate the lognormal assumption before relying on LOGINV calculations.
Alternatives
Modern replacement for LOGINV with identical functionality but better performance and compatibility with current Excel versions. Recommended for all new workbooks and forward compatibility.
When: Use LOGNORM.INV in Excel 2010 and later versions for the same lognormal inverse calculations. Provides better support and is the official recommended function.
Provides mathematical flexibility by calculating normal distribution inverse and then exponentiating the result. Allows custom transformations and greater control over calculations.
When: Use =EXP(NORM.INV(probability, mean, standard_dev)) when you need to combine normal distribution calculations with exponential transformations or when working with specific mathematical models.
Offers iterative approach to find x-values for specific probabilities, providing alternative methodology and validation of LOGINV results.
When: Use when validating LOGINV results or when you need to understand the underlying calculation process. Less efficient than LOGINV but useful for educational purposes and complex scenarios.
Compatibility
✓ Excel
Since 2007
=LOGINV(probability, mean, standard_dev) - Available in Excel 2007 and 2010. Replaced by LOGNORM.INV in Excel 2010+ but remains functional for backward compatibility.✗Google Sheets
Not available
✓LibreOffice
=LOGINV(probability, mean, standard_dev) - Fully supported in LibreOffice Calc with identical syntax and behavior to Excel.