Logarithmic series distribution
Density, distribution function, quantile function and random generation for the logarithmic series distribution.
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)
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[X ≤ x] otherwise, P[X > x]. |
p |
vector of probabilities. |
n |
number of observations. If |
Probability mass function
f(x) = (-1/log(1-θ)*θ^x) / x
Cumulative distribution function
F(x) = -1/log(1-θ) * sum((θ^x)/x)
Quantile function and random generation are computed using algorithm described in Krishnamoorthy (2006).
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.
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.