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Lognormal distribution
   UNDER CONSTRUCTION Draws the curves for the PDF and the CDF of a lognormal distribution.
 
Title A (preferably unique) title for the graph. •
Terminal style 1: "ps" & Times-Roman     2: "ppm", plot-likeGnuplot "terminal" style.
x0, λ (Valid now only for x0 = 0 .) Location parameter (≥ 0) and scale parameter (> 0).
σ Shape parameter (> 0).
xmax, m Graph goes from x0 to xmax, with m points.
Show values Shows the coordinates of the curve.
p A probability, to calculate x = F−1(p).
   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(Xx0) is Gaussian (μσ), 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
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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Created: 2004-01-07 — Last modified: 2007-10-13