The Lognormal Distribution

gsl_ran_lognormal(zeta, sigma)

This function returns a random variate from the lognormal distribution. The distribution function is,

\[p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} } \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx\]

for \(x > 0\).

gsl_ran_lognormal_pdf(x, zeta, sigma)

This function computes the probability density \(p(x)\) at \(x\) for a lognormal distribution with parameters zeta and sigma, using the formula given above.

gsl_cdf_lognormal_P(x, zeta, sigma)

gsl_cdf_lognormal_Q(x, zeta, sigma)

gsl_cdf_lognormal_Pinv(P, zeta, sigma)

gsl_cdf_lognormal_Qinv(Q, zeta, sigma)

These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the lognormal distribution with parameters zeta and sigma.

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The Flat (Uniform) Distribution

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The Chi-squared Distribution