Home / Statistical Tools / Distribution Fit/Calc / Distribution Fit / LogNormal Distribution
LogNormal Distribution (2-Parameter and 3-Parameter)¶
Distribution Fitting: Non-Reliability¶
From Excel click...
QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Fit > 2-Param LogNormal
From Excel click...
QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Fit > 3-Param LogNormal
Distribution Fitting: Reliability¶
Uncensored Data
From Excel click...
QXL Stat Tools Tab > Reliability > Uncensored > 2-Param LogNormal
From Excel click...
QXL Stat Tools Tab > Reliability > Uncensored > 3-Param LogNormal
Probability Calculator¶
From Excel click...
QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Calculator > LogNormal
The LogNormal distribution is a continuous probability distribution. If a random variable X has a LogNormal distribution, then Y=Ln(X) has a normal distribution. The LogNormal is sometimes called the Galton distribution.
| Parameters | \(-\infty < \mu < +\infty \quad \mu = \textit{Location}\) \(\sigma > 0 \quad \sigma = \textit{Scale}\) \(-\infty < \gamma < +\infty \quad \gamma = \textit{Offset (Threshold)}\) |
| Support | \(x \in (\gamma, +\infty)\) |
| Optimization parameter | \(\gamma = \textit{Offset (Threshold)}\) |
| Probability density function (pdf) | \(f(x) = \dfrac{1}{(x-\gamma)\sigma\sqrt{2\pi}}\, e^{-\frac{(\ln(x-\gamma)-\mu)^2}{2\sigma^2}}\) |