cdfln3 function

Three-parameter lognormal distribution

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))

Arguments

  • x: Vector of quantiles.

  • f: Vector of probabilities.

  • para: Numeric vector containing the parameters of the distribution, in the order zeta,mu,sigmazeta, mu, sigma

    (lower bound, mean on log scale, standard deviation on log scale).

Details

The three-parameter lognormal distribution with lower bound zetazeta, mean on log scale mumu, and standard deviation on log scale sigmasigma has distribution function

F(x)=Φ(y),F(x)=Phi(y), F(x)=\Phi(y),F(x) = Phi(y),

x>0x>0, where

y={log(xζ)μ}/\sigmay=(log(xzeta)mu)/sigma y=\lbrace\log(x - \zeta)-\mu\rbrace/\sigmay = (log(x-zeta) - mu) / sigma

and Phi(y)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 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)))
  • Maintainer: J. R. M. Hosking
  • License: Common Public License Version 1.0
  • Last published: 2024-09-30

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