The Double Log Normal Distribution

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Description

Density, distribution function, quantile function, random generation and expected value function for the double log normal distribution with mean equal to 'mean' and standard deviation equal to 'sd'.

Usage

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dloglognorm(x, mean = 0, sd = 1)
ploglognorm(q, mean = 0, sd = 1)
qloglognorm(p, mean = 0, sd = 1)
rloglognorm(n, mean = 0, sd = 1)
mloglognorm(moment, mean, sd)
eloglognorm(mean, sd)
vloglognorm(mean, sd)

Arguments

x,q

vector of quantiles.

p

vector of probabilites.

n

number of observations.

mean

vector of means.

sd

vector of standard deviations.

moment

vector of moments

Details

If 'mean' or 'sd' are not specified they assume the default values of '0' and '1', respectively.

Value

'dloglognorm' gives the density, 'ploglognorm' gives the distribution function, 'qloglognorm' gives the quantile function, 'rloglognorm' generates random deviates, 'mloglognorm' returns the rth moment, 'eloglognorm' gives the expected value of the distirbution and vloglognorm the variance.

Author(s)

Heike Trautmann trautmann@statistik.uni-dortmund.de, Detlef Steuer steuer@hsu-hamburg.de and Olaf Mersmann olafm@statistik.uni-dortmund.de

References

B. Holland, M. Ahsanullah (1989): Further Resultson the Distribution of Meinhold and Singpurwalla, The American Statistician 43 (4), p. 216-219

Examples

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  x <- seq(0, 1, by=0.05)
  ## Several different shapes of the density:
  par(mfrow=c(3, 1))
  curve(dloglognorm(x, -0.2, 0.2), 0, 1, main="DLN(-0.2, 0.2)")
  curve(dloglognorm(x,  0.2, 1.0), 0, 1, main="DLN(0.2, 2.0)")
  curve(dloglognorm(x,  0.2, 1.8), 0, 1, main="DLN(0.2, 2.0)")

  ## Check precision:
  z <- x - pnorm(qnorm(x, .2, 1.0), .2, 1.0)
  max(z)

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