How to use the LOGNORM.DIST function
What is the LOGNORM.DIST function?
The LOGNORMDIST function calculates the probabiltity based on the lognormal distribution of argument x, mean, and std_dev. This function has replaced the LOGNORMDIST function.
Table of Contents
1. Introduction
What is the lognormal distribution?
The lognormal distribution is a continuous probability distribution of a random variable whose logarithm follows a normal distribution. It is often used to model a steady relative growth rate is steady like financial returns.
What is the normally distributed ln(x)?
For a random variable x that follows a lognormal distribution like ln(x) is normally distributed. This means that if you take the natural logarithm of x the result will follow a standard normal distribution.
What is a continuous probability distribution?
A continuous probability distribution is defined over an interval and range of continuous values. This gives the probability an outcome that is exactly equal to any value, and having an area under its probability density curve equal to 1.
What is a continuous value?
A continuous value comes from a continuum of possible points rather than distinct separate values. It is able to take on any quantity within an interval rather than certain fixed outcomes.
2. Syntax
LOGNORM.DIST(x, mean, standard_dev, cumulative)
3. Arguments
| x | Required. |
| mean | Required. A value representing the mean of ln(x). |
| standard_dev | Required. A value representing the standard deviation of ln(x). |
| cumulative | Required. A boolean value determining the form of the function. TRUE - cumulative distribution function FALSE - probability density function |
What is the mean?
The arithmetic mean is calculated by dividing the sum of all values by the number of values.
For example, an array contains these values: 3,2,1
The sum is 3 + 2 + 1 equals 6
The number of values is 3.
6/3 equals 2. The average of 3, 2, 1 is 2
What is the standard deviation?
Standard deviation tells you how far from the average values are spread out. Both charts above have numbers and an average plotted, they share the same average however, the numbers are not the same.
Chart A above shows that the values are more spread out than the values in chart B. Chart A has a standard deviation of 23.45256334, standard deviation for chart B is 5.207075606. Standard deviation is used in statistics.
What is the cumulative distribution function?
The cumulative distribution function defines the probability that a random variable is less than or equal to a specified value. It gives the area under the probability density curve up to that value.
What is the probability density function?
A probability density function defines a continuous probability distribution by providing the relative likelihood that a random variable takes on different values. The total area under the curve over all values equal to 1.
4. Example 1
In a manufacturing process, the diameter of a particular component follows a lognormal distribution with a mean logarithm of 2.1 and a standard deviation of the logarithms of 0.3. What is the probability that a randomly selected component will have a diameter greater than 10 units?
The LOGNORM.DIST arguments are:
- x = 10
- mean = 2.1
- standard_dev = 0.3
- cumulative = true
The formula is LOGNORM.DIST(C16,C17,C18,C19) however we need the cumulative value for diameters above 10 units, not equal to and below 10 units. We need to calculate the complement by subtracting 1 with LOGNORM.DIST(C16,C17,C18,C19).
Formula in cell C7:
LOGNORM.DIST(C16,C17,C18,C19) returns approx. 0.75, 1 - LOGNORM.DIST(C16,C17,C18,C19) equals approx 0.25
The chart above shows blue columns representing the probability density function of the lognormal distribution and the black line represents the cumulative probability function.
In the image above, locate the value 10 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the black curve, which represents the cumulative distribution function. Then, follow the point of intersection horizontally towards the y-axis to the right. You will find that the corresponding value on the y-axis is approximately 0.75.
5. Example 2
The concentration of a certain pollutant in a river follows a lognormal distribution with a mean logarithm of 1.8 and a standard deviation of the logarithms of 0.2. What is the probability that a randomly sampled water sample will have a pollutant concentration exceeding the safe limit of 8 parts per million?
The LOGNORM.DIST arguments are:
- x = 8
- mean = 1.8
- standard_dev = 0.2
- cumulative = true
The formula is LOGNORM.DIST(C16,C17,C18,C19) however we need the cumulative value for concentrations above 8 ppm, not equal to and below 8 ppm. We need to calculate the complement by subtracting 1 with LOGNORM.DIST(C16,C17,C18,C19).
Formula in cell C7:
LOGNORM.DIST(C16,C17,C18,C19) returns approx. 0.92, 1 - LOGNORM.DIST(C16,C17,C18,C19) equals approx 0.08
The chart above shows blue columns representing the probability density function of the lognormal distribution and the black line represents the cumulative probability function.
In the image above, locate the value 8 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the black curve, which represents the cumulative distribution function. Then, follow the point of intersection horizontally towards the y-axis to the right. You will find that the corresponding value on the y-axis is approximately 0.92.
6. Example 3
The lifespans of a certain species of insect follow a lognormal distribution with a mean logarithm of 1.5 and a standard deviation of the logarithms of 0.3. What is the probability that a randomly selected insect will live for less than 6 weeks?
The LOGNORM.DIST arguments are:
- x = 6
- mean = 1.5
- standard_dev = 0.3
- cumulative = true
The formula is LOGNORM.DIST(C16,C17,C18,C19) however we need the cumulative value for the lifespan below 6 weeks.
Formula in cell C7:
LOGNORM.DIST(C16,C17,C18,C19) returns approx. 0.835
The chart above shows blue columns representing the probability density function of the lognormal distribution and the black line represents the cumulative probability function.
In the image above, locate the value 6 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the black curve, which represents the cumulative distribution function. Then, follow the point of intersection horizontally towards the y-axis to the right. You will find that the corresponding value on the y-axis is approximately 0.83.
7. Function not working
The LOGNORM.DIST function returns
- #VALUE! error value if any argument is non-numeric.
- #NUM! error value if:
- x <= 0
- standard_dev <= 0
7.1 Troubleshooting the error value
When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.
- The first line describes the error if you press with left mouse button on it.
- The second line opens a pane that explains the error in greater detail.
- The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
- This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
- The fifth line lets you edit the formula in the Formula bar.
- The sixth line opens the Excel settings so you can adjust the Error Checking Options.
Here are a few of the most common Excel errors you may encounter.
#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.
#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.
#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.
#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.
#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.
#NAME error - The #NAME error happens if you misspelled a function or a named range.
#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.
#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.
#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.
7.2 The formula returns an unexpected value
To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:
- Select the cell containing the formula you want to examine in detail.
- Go to tab “Formulas” on the ribbon.
- Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control. - Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
- Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
- Press "Close" button to dismiss the dialog box.
There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..
- Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
- Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
- Press F9: This will calculate and display the result of just that selected portion.
- Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
- Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.
The image above shows cell reference C3 converted to hard-coded value using the F9 key. The LOGNORM.DIST function requires numerical values in the first argument which is not the case in this example. We have found what is wrong with the formula.
Tips!
- View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
- Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
- Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.
Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button
7.3 Other errors
Floating-point arithmetic may give inaccurate results in Excel - Article
Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.
8. How is the function calculated
The equation to calculate the lognormal cumulative distribution is:
LOGNORM.DIST(x,µ,σ) = NORM.S.DIST(ln(x)-µ / σ)
Functions in 'Statistical' category
The LOGNORM.DIST function function is one of 73 functions in the 'Statistical' category.
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