This tool helps you calculate lognormal distribution values based on mean and standard deviation inputs.

## How to Use the Lognormal Distribution Calculator

To use this calculator:

- Enter the mean (μ) of your lognormal distribution.
- Enter the standard deviation (σ) of your lognormal distribution.
- Enter the value (x) you wish to evaluate.
- Click “Calculate” to get the result.

## How It Calculates the Result

The lognormal distribution calculator computes the probability density function (PDF) for a given value (x) using the mean (μ) and standard deviation (σ) of the lognormal distribution. The formula used is:

PDF(x, μ, σ) = (1 / (x * σ * sqrt(2 * π))) * exp(-((ln(x) - ln(μ))² / (2 * σ²)))

## Limitations

This calculator has certain limitations:

- The value (x) must be greater than 0.
- The standard deviation (σ) must be greater than 0.
- All inputs must be valid numeric values.

## Use Cases for This Calculator

### Calculate Probability of a Value

Enter the mean and standard deviation of a lognormal distribution, along with a specific value. The calculator will determine the probability of the value occurring in the given distribution, making it easy to understand the likelihood of that event.

### Estimate Value Given Probability

Input the mean and standard deviation of a lognormal distribution, as well as a desired probability. Get back the corresponding value at that probability level, helping you set realistic targets or thresholds based on the distribution.

### Determine Percentile Rank

Provide the mean and standard deviation of a lognormal distribution together with a value. The calculator will reveal the percentile rank of that value, showing you where it stands within the distribution range.

### Compare Two Values’ Probabilities

Supply the mean and standard deviation parameters for a lognormal distribution, and two separate values. The calculator will show you the probabilities of both values occurring in that particular distribution, aiding in decision-making or risk assessment.

### Forecast Future Value

Input the mean and standard deviation of a lognormal distribution, as well as a time period. The calculator will project a future value based on the distribution, guiding you in predicting outcomes or trends.

### Calculate Interval Probability

Enter the mean and standard deviation of a lognormal distribution, plus two values representing an interval. The calculator will compute the probability of values falling within that range, allowing you to assess uncertainty or confidence levels.

### Analyze Distribution Skewness

Provide the mean and standard deviation of a lognormal distribution. The calculator will display the skewness of the distribution, indicating the asymmetry of the data and helping you understand its shape.

### Understand Distribution Kurtosis

Input the mean and standard deviation of a lognormal distribution. The calculator will show you the kurtosis of the distribution, aiding in identifying whether data is heavy-tailed or light-tailed compared to a normal distribution.

### Sensitivity Analysis for Mean and Standard Deviation

Adjust the mean and standard deviation parameters of a lognormal distribution. The calculator will demonstrate how changes in these values impact the distribution’s shape, assisting you in sensitivity analysis and risk assessment.

### Enhance Investment Decision Making

By utilizing the lognormal distribution calculator with financial data, you can better analyze risks and potential returns of investments. This tool empowers you to make informed decisions backed by statistical insights and probability assessments.