dtplnorm {greybox}

Three Parameter Log Normal Distribution

Description

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.

Usage

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.

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.

Value

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.

Author(s)

Ivan Svetunkov, [e-mail]

References

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

See Also

Distributions

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)