TPLNormal function

Three Parameter Log Normal Distribution

Density, cumulative distribution, quantile functions and random number generation for the 3 parameter log normal distribution with the location parameter mu, scale sigma (which corresponds to standard deviation in normal distribution) and shifting parameter shift.

dtplnorm(q, mu = 0, sigma = 1, shift = 0, log = FALSE)

ptplnorm(q, mu = 0, sigma = 1, shift = 0)

qtplnorm(p, mu = 0, sigma = 1, shift = 0)

rtplnorm(n = 1, mu = 0, sigma = 1, shift = 0)

Arguments

• q: vector of quantiles.
• mu: vector of location parameters (means).
• sigma: vector of scale parameters.
• shift: vector of shift parameters.
• log: if TRUE, then probabilities are returned in logarithms.
• p: vector of probabilities.
• n: number of observations. Should be a single number.

Returns

Depending on the function, various things are returned (usually either vector or scalar):

• dtplnorm returns the density function value for the provided parameters.
• ptplnorm returns the value of the cumulative function for the provided parameters.
• qtplnorm returns quantiles of the distribution. Depending on what was provided in p, mu and sigma, this can be either a vector or a matrix, or an array.
• rtplnorm returns a vector of random variables generated from the tplnorm distribution. Depending on what was provided in mu and sigma, this can be either a vector or a matrix or an array.

Details

The distribution has the following density function:

f(x) = 1/(x-a) 1/sqrt(2 pi) exp(-(log(x-a)-mu)^2 / (2 sigma^2))

Both ptplnorm and qtplnorm are returned for the lower tail of the distribution.

The function is based on the lnorm functions from stats package, introducing the shift parameter.

Examples

x <- dtplnorm(c(-1000:1000)/200, 0, 1, 1)
plot(c(-1000:1000)/200, x, type="l")

x <- ptplnorm(c(-1000:1000)/200, 0, 1, 1)
plot(c(-1000:1000)/200, x, type="l")

qtplnorm(c(0.025,0.975), 0, c(1,2), 1)

x <- rtplnorm(1000, 0, 1, 1)
hist(x)

References

• Sangal, B. P., & Biswas, A. K. (1970). The 3-Parameter Distribution Applications in Hydrology. Water Resources Research, 6(2), 505–515. tools:::Rd_expr_doi("10.1029/WR006i002p00505")

See Also

Distributions

Author(s)

Ivan Svetunkov, ivan@svetunkov.com