Lognormal Distribution
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Calculate
Example: the time, in minutes, that visitors spend on a website has a normal logarithm, with μ = 1.5 and σ = 0.8. What is the chance that a visit lasts up to 10 minutes? Change the values to work out your own case.
Step by step
What each term means
- Density (f(x))
- The height of the curve at x > 0. The curve starts at zero, rises fast and falls slowly, with a long right tail.
- One in the Numerator
- Together with the denominator, it makes the total area under the curve equal 1.
- Normalization (xσ√(2π))
- The σ√(2π) is the normal's; the extra x comes from the change of scale from ln x to x, which stretches small values and squeezes large ones.
- Bell on a Log Scale
- The normal's bell, but in ln x: μ and σ are the mean and standard deviation of the logarithm, and e^μ is the median of x.