Draws the graph of a lognormal distribution.
The two curves, for the pdf and the cdf, are shown. The
value corresponding to a given cumulative distribution is calculated. (If
it is p = 1, 0 is assumed.)
If ln(X − x0) is Gaussian
(μ, σ), X is lognormal [Cramér, 1954, p
118; Dudewicz et al., 1988, p 176]. The mean and standard
deviation of X are
λX =
exp(λ+σ²⁄2) and
σX = λX
√[exp(σ²)−1] .
The following random variables can be represented by this distribution
[Meyer, 1972, p 219]: diameter of small particles after grinding; size of an
organism subjected to some small pulses; life time of certain
parts.
The formulas are: UNDER CONSTRUCTION |
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References:
• Cramér, Harald, 1954, "The elements of probability theory (and
some of its applications)", Almqvist & Wiksell, Stockholm (Sweden) (Wiley,
New York, NY, USA).
• Dudewicz, Edward J., Satya N. Mishra, 1988, "Modern mathematical
Statistics", J. Wiley & Sons, New York, NY (USA).
• Meyer, Paul L., 1972, «Probabilidade, aplicações à
Estatística», Ed. Ao Livro Técnico, Rio de Janeiro, GB (Brasil).
• NIST/SEMATECH, 2004-01-08,
"Lognormal distribution", e-Handbook of Statistical Methods,
http://www.itl.nist.gov/div898/handbook.
(ITL,
US NIST)
• Weisstein, Eric W., 2004-01-08,
"Lognormal
distribution", Eric Weisstein's World of Mathematics,
http://mathworld.wolfram.com/LogNormalDistribution.html.
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