LogSeries {extraDistr} | R Documentation |
Logarithmic series distribution
Description
Density, distribution function, quantile function and random generation for the logarithmic series distribution.
Usage
dlgser(x, theta, log = FALSE)
plgser(q, theta, lower.tail = TRUE, log.p = FALSE)
qlgser(p, theta, lower.tail = TRUE, log.p = FALSE)
rlgser(n, theta)
Arguments
x , q |
vector of quantiles. |
theta |
vector; concentration parameter; ( |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. If |
Details
Probability mass function
Cumulative distribution function
Quantile function and random generation are computed using algorithm described in Krishnamoorthy (2006).
References
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC
Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.
Examples
x <- rlgser(1e5, 0.66)
xx <- seq(0, 100, by = 1)
plot(prop.table(table(x)), type = "h")
lines(xx, dlgser(xx, 0.66), col = "red")
# Notice: distribution of F(X) is far from uniform:
hist(plgser(x, 0.66), 50)
xx <- seq(0, 100, by = 0.01)
plot(ecdf(x))
lines(xx, plgser(xx, 0.66), col = "red", lwd = 2)