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))
Arguments
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).
Details
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)=Φ(y),F(x)=Phi(y),
x>0, where
y={log(x−ζ)−μ}/\sigmay=(log(x−zeta)−mu)/sigma
and Phi(y) is the distribution function of the standard normal distribution.
Returns
cdfln3 gives the distribution function; qualn3 gives the quantile function.
Note
The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard
distribution functions pnorm, qnorm, etc.
See Also
cdfgno for the generalized normal distribution, a more general form of the three-parameter lognormal distribution.
qlnorm for the standard version of the two-parameter lognormal distribution.
Examples
# 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 distributionxx <- qualn3(runif(50))# Fit 2-parameter LN distributionpelln3(samlmu(xx), bound=0)# Fit 2-parameter LN distribution "in log space",# i.e. fit normal distribution to log-transformed datapelnor(samlmu(log(xx)))