Lognormal distribution Probabilities
Calculator of Lognormal distribution : probabilities, density function (PDF) and cumulative density function (CDF).
Lognormal Distribution formulas
X : a random variable following a lognormal distribution
`mu` : first parameter
`sigma` : second parameter ( > 0)
Probability Density Function (PDF)
`f(x) = 1/(x*sigma*sqrt(2*pi))*exp(-(ln(x)-mu)^2/(2*sigma^2))` for `x > 0`
Cumulative distribution function (CDF)
`F(x) = \int_0^x f(t)\ dt`
`F(x) = 1/2*(1+\text{erf}((ln(x)-mu)/(sigma*sqrt(2))))` for `x > 0`
where erf is the Error function,
`\text{erf}(x) = 2/sqrt(pi)*\int_0^x e^(-t^2)\ dt`
Probabilities
Probability that X is greater than a :
`P(X > a) = 1 - F(a)`
Probability that X is less than b :
`P(X < b) = F(b)`
Probability that X lies between a and b :
`P(a < X < b) = F(b) - F(a)`
See also
Inverse Lognormal distribution
Lognormal distribution Chart
Statistics Calculators