Three-parameter lognormal distribution
Distribution function and quantile function of the three-parameter lognormal distribution.
cdfln3(x, para = c(0, 0, 1)) qualn3(f, para = c(0, 0, 1))
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
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),
x>0, where
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
distribution functions pnorm, qnorm, etc.
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.
# 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)))
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