Distribution function and quantile function of the three-parameter lognormal distribution.
Vector of quantiles.
Vector of probabilities.
Numeric vector containing the parameters of the distribution, in the order zeta, mu, sigma (lower bound, mean on log scale, standard deviation on log scale).
The three-parameter lognormal distribution with lower bound zeta, mean on log scale mu, and standard deviation on log scale sigma has distribution function
F(x) = Phi(y),
y = (log(x-zeta) - mu) / sigma
and Phi(y) is the distribution function of the standard normal distribution.
cdfln3 gives the distribution function;
qualn3 gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
cdfgno for the generalized normal distribution,
a more general form of the three-parameter lognormal distribution.
qlnorm for the standard R version of the
two-parameter lognormal distribution.
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# Random sample from three-parameter lognormal distribution # with parameters zeta=0, mu=1, sigma=0.5. qualn3(runif(100), c(0,1,0.5)) ## Functions for the three-parameter lognormal distribution can ## also be used with the two-parameter lognormal distribution # Generate a random sample from a standard lognormal distribution xx <- qualn3(runif(50)) # Fit 2-parameter LN distribution pelln3(samlmu(xx), bound=0) # Fit 2-parameter LN distribution "in log space", # i.e. fit normal distribution to log-transformed data pelnor(samlmu(log(xx)))