Stat
Dist
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Distribution
Beta
Binomial
Cauchy
Chi-squared
Erlang
Exponential
F
Gamma
Laplace
Levy
Logarithmic
Logistic
Log-logistic
Log-normal
Negative Binomial
Normal
Pareto
Poisson
Rayleigh
Student's T
Triangular
Uniform
Weibull
μ
mean
Real number.
σ
se
Real number greater than 0.
Details
Parameters
Mean
μ
∈ ℝ
Scale
σ
> 0
Support
x
∈ (0, ∞)
PDF
1
x
σ
√
2
π
e
−
(ln
x
−
μ
)
2
2
σ
2
CDF
Φ
ln
x
−
μ
σ
where
Φ
is the CDF of the standard normal distribution.
Mean
e
μ
+
σ
2
/ 2
Variance
(
e
σ
2
− 1)
e
2
μ
+
σ
2
Skewness
√
e
σ
2
− 1
(
e
σ
2
+ 2)
Excess kurtosis
2
e
2
σ
2
+ 2
e
3
σ
2
+
e
4
σ
2
− 3
Enter parameter values above to view the Log-normal probability density and cumulative distribution functions
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