Logarithmic Distribution

Density, distribution function, quantile function, and random generation for the logarithmic distribution.

Usage

dlog(x, shape, log = FALSE)
plog(q, shape, lower.tail = TRUE, log.p = FALSE)
qlog(p, shape)
rlog(n, shape)

Arguments

x, q, p, n, lower.tail

Same interpretation as in runif.

shape

The shape parameter value \(c\) described in in logff.

log, log.p

Logical. If log.p = TRUE then all probabilities p are given as log(p).

Details

The details are given in logff.

Value

dlog gives the density, plog gives the distribution function, qlog gives the quantile function, and rlog generates random deviates.

References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

Author

T. W. Yee

Note

Given some response data, the VGAM family function logff estimates the parameter shape. For plog(), if argument q contains large values and/or q is long in length then the memory requirements may be very high. Very large values in q are handled by an approximation by Owen (1965).

Examples

dlog(1:20, 0.5)
#>  [1] 7.213475e-01 1.803369e-01 6.011229e-02 2.254211e-02 9.016844e-03
#>  [6] 3.757018e-03 1.610151e-03 7.044409e-04 3.130849e-04 1.408882e-04
#> [11] 6.404009e-05 2.935171e-05 1.354694e-05 6.289651e-06 2.935171e-06
#> [16] 1.375861e-06 6.474641e-07 3.057469e-07 1.448275e-07 6.879306e-08
rlog(20, 0.5)
#>  [1] 1 1 1 1 1 1 1 2 2 1 1 1 1 1 3 1 1 1 1 2

if (FALSE)  shape <- 0.8; x <- 1:10
plot(x, dlog(x, shape = shape), type = "h", ylim = 0:1,
     sub = "shape=0.8", las = 1, col = "blue", ylab = "shape",
     main = "Logarithmic distribution: blue=PDF; orange=CDF")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'y' in selecting a method for function 'plot': object 'shape' not found
lines(x + 0.1, plog(x, shape), col = "orange", lty = 3, type = "h")  # \dontrun{}
#> Error: object 'shape' not found