### 20.16 The Lognormal Distribution

— Function: double gsl_ran_lognormal (const gsl_rng * r, double zeta, double 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.

— Function: double gsl_ran_lognormal_pdf (double x, double zeta, double 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.

— Function: double gsl_cdf_lognormal_P (double x, double zeta, double sigma)
— Function: double gsl_cdf_lognormal_Q (double x, double zeta, double sigma)
— Function: double gsl_cdf_lognormal_Pinv (double P, double zeta, double sigma)
— Function: double gsl_cdf_lognormal_Qinv (double Q, double zeta, double 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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