Calculadora de Distribuição Lognormal (E[X])

The Lognormal Distribution Calculator computes the expected value (mean) of a random variable that follows a lognormal distribution. Unlike the normal distribution, where the variable is symmetric, in the lognormal distribution values are always positive and the distribution is right-skewed. The formula used is E[X] = exp(μ + σ²/2), where μ is the mean of the logarithms of the data and σ is the standard deviation of the logarithms. This tool is useful for those working with financial data, such as stock prices, or in engineering, where quantities like failure time are modeled by this distribution.

To use the calculator, simply enter the values of μ (mean of logs) and σ (standard deviation of logs) in the appropriate fields. The result displays the mean of the original distribution. It is important to remember that μ and σ are not the mean and standard deviation of the raw data, but rather of the data transformed by the natural logarithm. For example, if you have income data that follows a lognormal distribution, μ and σ are calculated from the logarithm of income.

When to use this calculator? In finance, to estimate the expected return of assets whose prices follow a geometric Brownian motion. In reliability studies, to calculate the mean time to failure of components. It is also useful in areas such as biology, for modeling organism sizes, and in meteorology, for precipitation. Caution: the lognormal distribution is sensitive to extreme values; make sure your data actually fits it before using the formula.

Common pitfalls: do not confuse μ and σ with the mean and standard deviation of the original data. Also, the formula assumes that the logs of the data are normally distributed. If there are zeros or negative values, the lognormal distribution is not applicable. Always check the suitability of the model to your data.